Willox Ralph ＷＩＬＬＯＸＲａｌｐｈ

… Alternative Names

WILLOX Ralph ウィロックスラルフ

RALPH WILLOX ラルフウイロツクス

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Researcher Number	20361610
Other IDs
Affiliation (Current)	2025: 東京大学, 大学院数理科学研究科, 教授
Affiliation (based on the past Project Information) *help	2016 – 2024: 東京大学, 大学院数理科学研究科, 教授 2015: 東京大学, 数理科学, 准教授 2015: 東京大学, 数理科学研究科, 教授 2014 – 2015: 東京大学, 数理(科)学研究科(研究院), 教授 2013: 東京大学, 大学院数理科学研究科, 准教授 … More 2012 – 2013: 東京大学, 数理(科)学研究科(研究院), 准教授 2007 – 2011: The University of Tokyo, Graduate School of Mathematical Sciences, Associate professor 2006: 東京大学, 大学院数理科学研究科, 助教授 2004 – 2005: 東京大学, 大学院・数理科学研究科, 助教授 Less
Review Section/Research Field	Principal Investigator Global analysis / Basic Section 12020:Mathematical analysis-related / Basic Section 12020:Mathematical analysis-related / Basic analysis Except Principal Investigator Global analysis / Risk sciences of radiation and chemicals
Keywords	Principal Investigator 離散可積分系 / 可積分系 / セルオートマトン / 特異点 / エントロピー / 関数方程式 / 超離散可積分系 / セル・オートマトン / 離散系 / 非線形変差分方程式 … More / 遅延型微分方程式 / 特異点閉じ込め / 離散化 / 非自励系 / 力学系次数 / 双有理写像 / 特異点閉じ込め方 / ダルブー変換 / ベックルンド変換 / 離散パンルヴェ方程式 / QRT写像 / Miura変換 / 特異点閉じ込め法 / ソリトン現象 / 超離散系 / 超離散極限 / 離散力学系 / 差分方程式 / パンルヴェ方程式 … More Except Principal Investigator 可積分系 / ソリトン / 箱玉系 / 超離散系 / セルオートマトン / 生物影響 / がん遺伝子 / 超離散化 / 特殊関数 / Toda equation / tropical geometry / integrable lattice model / quantum algebra / Box-Ball System / Cellular Automaton / ultradiscrete integrable system / discrete integrable system / セルオートマン / 逆超離散化 / クリスタル / 離散系 / 戸田方程式 / トロピカル幾何 / 可解格子模型 / 量子代数 / 超離散可積分系 / 離散可積分系 / トロピカル / 特異値閉じ込め / トロピカル曲線 / 有限体 Less

Extending the geometric theory of discrete Painleve equations - singularities, entropy and integrabilityPrincipal Investigator
- Principal Investigator
  
  WILLOX Ralph
- Project Period (FY)
  2022 – 2023
- Research Category
  
  Grant-in-Aid for JSPS Fellows
- Review Section
  
  Basic Section 12020:Mathematical analysis-related
- Research Institution
  The University of Tokyo
ntegrability of nonlinear partial difference and functional equations: a singularity and entropy based approachPrincipal Investigator
- Principal Investigator
  
  WILLOX Ralph
- Project Period (FY)
  2022 – 2025
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Review Section
  
  Basic Section 12020:Mathematical analysis-related
- Research Institution
  The University of Tokyo
Classification and characterization of the integrability of rational difference equations based on their dynamical degreePrincipal Investigator
- Principal Investigator
  
  WILLOX RALPH
- Project Period (FY)
  2018 – 2021
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 12020:Mathematical analysis-related
- Research Institution
  The University of Tokyo
Algebraic and geometric properties of discrete integrable systemsPrincipal Investigator
- Principal Investigator
  
  Willox Ralph
- Project Period (FY)
  2015 – 2017
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  The University of Tokyo
Evaluation of radiation effect based on point mutation of BRAF gene
- Principal Investigator
  
  Wada Youichiro
- Project Period (FY)
  2015
- Research Category
  
  Grant-in-Aid for Challenging Exploratory Research
- Research Field
  
  Risk sciences of radiation and chemicals
- Research Institution
  The University of Tokyo
Towards a unified research method for ultradiscrete integrable systemsPrincipal Investigator
- Principal Investigator
  
  WILLOX Ralph
- Project Period (FY)
  2012 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Global analysis
- Research Institution
  The University of Tokyo
Extension of special functions from the viewpoint of integrable systems
- Principal Investigator
  
  KAKEI Saburo
- Project Period (FY)
  2011 – 2015
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Global analysis
- Research Institution
  Rikkyo University
Study on the integrable structure of ultradiscrete systems
- Principal Investigator
  
  TOKIHIRO Tetsuji
- Project Period (FY)
  2009 – 2012
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Global analysis
- Research Institution
  The University of Tokyo
Direct methods for ultradiscrete systemsPrincipal Investigator
- Principal Investigator
  
  WILLOX Ralph
- Project Period (FY)
  2009 – 2011
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Global analysis
- Research Institution
  The University of Tokyo
Study of methods for analysing continuous systems, relying ondiscrete and ultra-discrete systemsPrincipal Investigator
- Principal Investigator
  
  WILLOX Ralph
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Global analysis
- Research Institution
  The University of Tokyo
リダクションによるパンルヴェ方程式の研究Principal Investigator
- Principal Investigator
  
  RALPH WILLOX (WILLOX Ralph)
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Global analysis
- Research Institution
  The University of Tokyo
Mathematics on discrete and ultradiscrete integrable systems and its application
- Principal Investigator
  
  TOKIHIRO Tetsuji
- Project Period (FY)
  2004 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Global analysis
- Research Institution
  The University of Tokyo

[Book] Detecting discrete integrability: the singularity approach, in ``Nonlinear Systems and Their Remarkable Mathematical Structures: Volume I"2018
- Author(s)
  B. Grammaticos, A. Ramani, R. Willox and T. Mase
- Publisher
  CRC Press, Boca Raton FL
- ISBN
  9781138601000
- Data Source
  KAKENHI-PROJECT-18K03355
[Book] Special function solutions for integrable nonlinear PDE's(Gakkotosho International Series - Mathematical Sciences and Applications Vol.22)2005
- Author(s)
  R.Willox
- Data Source
  KAKENHI-PROJECT-16740088
[Journal Article] Singularities and growth of higher order discrete equations2024
- Author(s)
  Willox Ralph、Mase Takafumi、Ramani Alfred、Grammaticos Basil
- Journal Title
  
  Open Communications in Nonlinear Mathematical Physics
  
  Volume: Special Issue 2
- DOI
  10.46298/ocnmp.13267
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K22401
[Journal Article] Full-deautonomisation of a class of second-order mappings in ancillary form2023
- Author(s)
  Grammaticos Basil、Willox Ralph
- Journal Title
  
  Open Communications in Nonlinear Mathematical Physics
  
  Volume: Volume 3
- DOI
  10.46298/ocnmp.10496
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K22401
[Journal Article] On the singularity structure of a discrete modified-Korteweg-deVries equation2022
- Author(s)
  Grammaticos Basil、Tamizhmani Thamizharasi、Willox Ralph
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 55 Issue: 26 Pages: 265203-265203
- DOI
  10.1088/1751-8121/ac711b
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K22401
[Journal Article] On the singularities of the discrete Korteweg-de Vries equation2021
- Author(s)
  Um D.、Ramani A.、Grammaticos B.、Willox R.、Satsuma J.
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 54 Issue: 9 Pages: 095201-095201
- DOI
  10.1088/1751-8121/abd8f4
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] 可積分な場合のHenon-Heiles系の離散化2021
- Author(s)
  H. Iino, R. Willox
- Journal Title
  
  津田塾大学　数学・計算機科学研究報
  
  Volume: 42 Pages: 135-140
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] Discretising and ultradiscretising the “Human and Nature Dynamics Model” - new challenges and the limits of modelling -2021
- Author(s)
  R. Willox
- Journal Title
  
  Reports of Institute for Mathematics and Computer Science, Tsuda University
  
  Volume: 42 Pages: 1-16
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] Revisiting the Human and Nature Dynamics Model2020
- Author(s)
  Grammaticos Basil、Willox Ralph、Satsuma Junkichi
- Journal Title
  
  Regular and Chaotic Dynamics
  
  Volume: 25 Issue: 2 Pages: 178-198
- DOI
  10.1134/s1560354720020045
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] Discrete Painleve equations from singularity patterns: The asymmetric trihomographic case2020
- Author(s)
  B. Grammaticos, A. Ramani, R. Willox and J. Satsuma
- Journal Title
  
  Journal of Mathematical Physics
  
  Volume: 61 Issue: 3
- DOI
  10.1063/1.5115023
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] On the singularity structure of the discrete KdV equation2020
- Author(s)
  D. Um, R. Willox, B. Grammaticos and A. Ramani
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 53 Issue: 11 Pages: 114001-114001
- DOI
  10.1088/1751-8121/ab72af
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] Algebraic entropy computations for lattice equations: why initial value problems do matter2019
- Author(s)
  J. Hietarinta, T. Mase and R. Willox
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 52 Issue: 49 Pages: 49LT01-49LT01
- DOI
  10.1088/1751-8121/ab5238
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355, KAKENHI-PROJECT-18K13438
[Journal Article] Singularity confinement as an integrability criterion2019
- Author(s)
  Mase Takafumi、Willox Ralph、Ramani Alfred、Grammaticos Basil
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 52 Issue: 20 Pages: 205201-205201
- DOI
  10.1088/1751-8121/ab1433
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355, KAKENHI-PROJECT-18K13438
[Journal Article] Restoring discrete Painleve equations from an E_8^(1)-associated one2019
- Author(s)
  B. Grammaticos, A. Ramani and R. Willox
- Journal Title
  
  Journal of Mathematical Physics
  
  Volume: 60 Issue: 6
- DOI
  10.1063/1.5084005
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] Constructing discrete Painlev\'e equations: from E$_8^{(1)}$ to A$_1^{(1)}$ and back2019
- Author(s)
  A. Ramani, B. Grammaticos, R. Willox and T. Tamizhmani
- Journal Title
  
  Journal of Nonlinear Mathematical Physics
  
  Volume: 掲載確定
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] Darboux dressing and undressing for the ultradiscrete KdV equation2019
- Author(s)
  J.J.C. Nimmo, C.R. Gilson and R. Willox
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 52 Issue: 44 Pages: 445201-445201
- DOI
  10.1088/1751-8121/ab45cf
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Journal Article] Singularity patterns and dynamical degrees2018
- Author(s)
  Mase T., Willox R., Ramani A., Grammaticos B.
- Journal Title
  
  九州大学応用力学研究所・研究集会報告書・非線形波動研究の新潮流 - 理論と応用 -
  
  Volume: 未定
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893
[Journal Article] Linearization of the box-ball system: an elementary approach2018
- Author(s)
  Saburo Kakei, Jonathan J.C. Nimmo, Satoshi Tsujimoto, Ralph Willox
- Journal Title
  
  Journal of Integrable Systems
  
  Volume: 3 Issue: 1 Pages: 1-32
- DOI
  10.1093/integr/xyy002
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05184, KAKENHI-PROJECT-16K13761, KAKENHI-PROJECT-15K04893
[Journal Article] Calculating algebraic entropies: an express method2017
- Author(s)
  A. Ramani, B. Grammaticos, R. Willox and T. Mase
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 50 Issue: 18 Pages: 185203-185203
- DOI
  10.1088/1751-8121/aa66d7
- Peer Reviewed / Acknowledgement Compliant / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893, KAKENHI-PROJECT-16H06711
[Journal Article] A systematic method for constructing discrete Painleve equations in the degeneration cascade of the E8 group2017
- Author(s)
  Willox R.、Ramani A.、Grammaticos B.
- Journal Title
  
  Journal of Mathematical Physics
  
  Volume: 58 Issue: 12
- DOI
  10.1063/1.5004764
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893
[Journal Article] Miura transformations for discrete Painleve equations coming from the affine E_8 Weyl group2017
- Author(s)
  A. Ramani, B. Grammaticos and R. Willox
- Journal Title
  
  Journal of Mathematical Physics
  
  Volume: 58 Issue: 4
- DOI
  10.1063/1.4979794
- Peer Reviewed / Acknowledgement Compliant / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893
[Journal Article] Multiplicative equations related to the affine Weyl group E82017
- Author(s)
  B.Grammaticos, A.Ramani, R Willox and J. Satsuma
- Journal Title
  
  J. Math. Phys.
  
  Volume: 58 Issue: 8 Pages: 083502-083502
- DOI
  10.1063/1.4997166
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05048, KAKENHI-PROJECT-15K04893
[Journal Article] Full-deautonomisation of a lattice equation2016
- Author(s)
  R. Willox, T. Mase, A. Ramani and B. Grammaticos
- Journal Title
  
  Journal of Physics A: Mathematical and Theoretical
  
  Volume: 49 Issue: 28 Pages: 28LT01-28LT01
- DOI
  10.1088/1751-8113/49/28/28lt01
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16H06711, KAKENHI-PROJECT-15K04893
[Journal Article] Burchnall-Chaundy polynomials and the Laurent phenomenon2015
- Author(s)
  A.P. Veselov and R. Willox
- Journal Title
  
  Journal of Physics A: Math. Theor.
  
  Volume: 48
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540204
[Journal Article] Singularity confinement and full-deautonomisation: a discrete integrability criterion2015
- Author(s)
  B. Grammaticos, A. Ramani, R. Willox, T. Mase and J. Satsuma
- Journal Title
  
  Physica D
  
  Volume: 313 Pages: 11-25
- DOI
  10.1016/j.physd.2015.09.006
- Peer Reviewed / Acknowledgement Compliant / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893, KAKENHI-PROJECT-13J03088
[Journal Article] The redemption of singularity confinement2015
- Author(s)
  間瀬崇史
- Journal Title
  
  Journal of Physics A : Mathematical and Theoretical
  
  Volume: 48 Issue: 11 Pages: 11FT02-11FT02
- DOI
  10.1088/1751-8113/48/11/11ft02
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-13J03088, KAKENHI-PROJECT-14J00242, KAKENHI-PROJECT-24540204
[Journal Article] Deautonomisation by singularity confinement: an algebro-geometric justification2015
- Author(s)
  T. Mase, R. Willox, B. Grammaticos and A. Ramani
- Journal Title
  
  Proceedings of the Royal Society A
  
  Volume: 471 Issue: 2183 Pages: 20140956-20140956
- DOI
  10.1098/rspa.2014.0956
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893, KAKENHI-PROJECT-13J03088
[Journal Article] The ultradiscrete sine-Gordon equation: introducing the oiston2014
- Author(s)
  R. Willox, A. Ramani and B. Grammaticos
- Journal Title
  
  「非線形波動研究の拡がり」, 九州大学応用力学研究所研究集会報告
  
  Volume: No.25AO-S2 Pages: 29-34
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540204
[Journal Article] Discretisations of constrained KP hierarchies2014
- Author(s)
  R. Willox and M. Hattori
- Journal Title
  
  the Journal of Mathematical Sciences, the University of Tokyo
  
  Volume: 印刷中
- NAID
  120005819508
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540204
[Journal Article] Solutions of the lattice sine-Gordon equation and the solitons of its cellular automaton2014
- Author(s)
  R. Willox, A. Ramani and B. Grammaticos
- Journal Title
  
  Journal of Physics A: Math. Theor.
  
  Volume: 47 Issue: 12 Pages: 125202-125202
- DOI
  10.1088/1751-8113/47/12/125202
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24540204
[Journal Article] 拡張されたTzitzeica方程式と中心等積アフィン曲面2013
- Author(s)
  三谷浩将，筧三郎，Ralph Willox
- Journal Title
  
  九州大学応用力学研究所研究集会報告
  
  Volume: 24AO-S3 Pages: 128-133
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540252
[Journal Article] Discretising the Painlev´e equations ‵a la Hirota-Mickens2012
- Author(s)
  B. Grammaticos, A. Ramani, J. Satsuma and R. Willox
- Journal Title
  
  J. Math. Phys
  
  Volume: 53 Issue: 2 Pages: 24-24
- DOI
  10.1063/1.3682240
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21340034, KAKENHI-PROJECT-21540210, KAKENHI-PROJECT-21560069
[Journal Article] On Quispel-Roberts-Thompson extensions and inte-grable correspondences2011
- Author(s)
  B. Grammaticos, A. Ramani, K. M. Tamizhani and R. Willox
- Journal Title
  
  Journal of Mathematical Physics
  
  Volume: 52 Issue: 5 Pages: 11-11
- DOI
  10.1063/1.3588166
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540210
[Journal Article] Generalised QRT mappings with periodic coefficients2011
- Author(s)
  A. Ramani, B. Grammaticos and R. Willox
- Journal Title
  
  Nonlinearity
  
  Volume: 24 Issue: 1 Pages: 113-126
- DOI
  10.1088/0951-7715/24/1/006
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540210
[Journal Article] Miura trans-formations and the various guises of integrable lattice equations2011
- Author(s)
  B. Grammaticos, A. Ramani, C. Scimiterna and R. Willox
- Journal Title
  
  Journal of Physics A : Mathematical and Theoretical
  
  Volume: 44 Issue: 15 Pages: 9-9
- DOI
  10.1088/1751-8113/44/15/152004
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540210
[Journal Article] FOLDING TRANSFORMATIONS AND HKY MAPPINGS2011
- Author(s)
  B. GRAMMATICOS, A. RAMANI and R. WILLOX
- Journal Title
  
  Journal of Nonlinear Mathematical Physics
  
  Volume: 18 Issue: 1 Pages: 75-85
- DOI
  10.1142/s1402925111001179
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21340034, KAKENHI-PROJECT-21540210
[Journal Article] Solving the ultradiscrete KdV equation2010
- Author(s)
  R.Willox, et al.
- Journal Title
  
  Journal of Physics A : Math.and Theor.
  
  Volume: 43
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540210
[Journal Article] Solving the ultradiscrete KdV equation2010
- Author(s)
  Ralph Willox, Yoichi Nakata, Junkichi Satsuma, Alfred Ramani and Basile Grammaticos
- Journal Title
  
  J. Phys. A : Math. Theor
  
  Volume: 43 Issue: 48 Pages: 7-7
- DOI
  10.1088/1751-8113/43/48/482003
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21340034, KAKENHI-PROJECT-21540210, KAKENHI-PROJECT-21560069
[Journal Article] Yang-Baxter maps from the discrete BKP equation2010
- Author(s)
  S. Kakei, J. J. C. Nimmo and R. Willox
- Journal Title
  
  SIGMA
  
  Volume: 6 Pages: 11-11
- DOI
  10.3842/sigma.2010.028
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540210
[Journal Article] Yang-Baxter maps and the discrete Kphierarchy2009
- Author(s)
  S. Kakei, J.J.C. Nimmo, R. Willox
- Journal Title
  
  Glasgow Mathematical Journal 51A
  
  Pages: 107-119
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540204
[Journal Article] On two (not so) new integrablepartial difference equations2009
- Author(s)
  A. Ramani, B. Grammaticos, J. Satsuma, R. Willox
- Journal Title
  
  Journal ofPhysics A : Mathematical and Theoretical 掲載決定済み
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540204
[Journal Article] Bilinearisation and solutions of the KdV6equation2008
- Author(s)
  A. Ramani, B. Grammaticos, R. Willox
- Journal Title
  
  Analysis and Applications 6
  
  Pages: 401-412
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540204
[Journal Article] Contiguity relations for discrete andultradiscrete Painleve equation2008
- Author(s)
  A. Ramani, B. Grammaticos, R. Willox
- Journal Title
  
  Journalof Nonlinear Mathematical Physics 15
  
  Pages: 353-364
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540204
[Journal Article] Discretisation-induced delaysand their role in the dynamics2008
- Author(s)
  A. Ramani, B. Grammaticos, J. Satsuma, R. Willox
- Journal Title
  
  Journal ofPhysics A : Mathematical and Theoretical 41
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540204
[Journal Article] Constructinglump-like solutions of the Hirota-Miwaequation2007
- Author(s)
  B. Grammaticos, A. Ramani, V. Papageorgiou, J. Satsuma, R. Willox
- Journal Title
  
  Journal of Physics A : Mathe-matical and Theoretical 40
  
  Pages: 12619-12627
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540204
[Journal Article] From limit cycles to periodic orbits through ultradiscretisation2007
- Author(s)
  R. Willox, et. al.
- Journal Title
  
  Physica A 385
  
  Pages: 473-486
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540204
[Journal Article] From limit cycles to periodic orbits through ultradiscretisation2007
- Author(s)
  R. Willox
- Journal Title
  
  Physica A 385
  
  Pages: 473-486
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16204009
[Journal Article] From limit cycles to periodicorbits through ultradiscretisation2007
- Author(s)
  R. Willox, A. Ramani, J. Satsuma, B.Grammaticos
- Journal Title
  
  Physica A 385
  
  Pages: 473-486
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540204
[Journal Article] From limit cycles to periodic orbits through ultradiscretisation2007
- Author(s)
  R. Willox
- Journal Title
  
  Physica A Vol. 385
  
  Pages: 273-486
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16204009
[Journal Article] A study of the antisymmetric QRT mappings2005
- Author(s)
  R.Willox
- Journal Title
  
  Journal of Physics A 38
  
  Pages: 5227-5236
- Data Source
  KAKENHI-PROJECT-16740088
[Journal Article] On a generalized Tzitzeica equation2005
- Author(s)
  R.Willox
- Journal Title
  
  Glasgow Mathematical Journal 47a(発表予定)
- Data Source
  KAKENHI-PROJECT-16740088
[Journal Article] On a generalized Tzitzeica equation2005
- Author(s)
  R.Willox
- Journal Title
  
  Glasgow Mathematical Journal 47a
  
  Pages: 221-231
- Data Source
  KAKENHI-PROJECT-16740088
[Journal Article] A KdV cellular auto-maton without integers
- Author(s)
  R. Willox, A. Ramani, J. Satsuma and B. Grammaticos
- Journal Title
  
  Contemporary Mathematics
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] Testing for integrability using the full-deautonomisation method2023
- Author(s)
  Ralph Willox
- Organizer
  Dualities and Symmetries in Integrable Systems
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K22401
[Presentation] The singularity structure of the discrete KdV and mKdV equations2023
- Author(s)
  Ralph Willox
- Organizer
  SIDE14.2: Symmetries and Integrability of Difference Equations
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K22401
[Presentation] Direct and inverse scattering for the ultradiscrete KdV equation2022
- Author(s)
  Ralph Willox
- Organizer
  Workshop on box-ball systems from integrable systems and probabilistic perspectives `September 19-23, 2022', CRM, Montreal, Canada
- Invited
- Data Source
  KAKENHI-PROJECT-23K22401
[Presentation] The singularity structure of integrable lattice equations2021
- Author(s)
  Ralph Willox
- Organizer
  Integrable Systems 2021
- Invited
- Data Source
  KAKENHI-PROJECT-18K03355
[Presentation] Discretising and ultradiscretising the “Human and Nature Dynamics Model” ー new challenges and the limits of modelling2020
- Author(s)
  Ralph Willox
- Organizer
  From Nonlinear Waves to Integrable Systems
- Invited
- Data Source
  KAKENHI-PROJECT-18K03355
[Presentation] On the direct and inverse scattering problems for udKdV2019
- Author(s)
  R. Willox
- Organizer
  China-Japan Joint Workshop on Integrable Systems 2019, Hayama, Japan
- Data Source
  KAKENHI-PROJECT-18K03355
[Presentation] Integrability tests for lattice equations - or why lattice equations are more interesting (and subtle) than ordinary mappings2019
- Author(s)
  R. Willox
- Organizer
  Integrable Systems 2019, The University of Sydney, Australia
- Invited
- Data Source
  KAKENHI-PROJECT-18K03355
[Presentation] Solution to the direct and inverse scattering problems for the ultradiscrete KdV equation2019
- Author(s)
  R. Willox
- Organizer
  Integrable systems, special functions and combinatorics, Sabhal Mor Ostaig -- the Gaelic College, the Isle of Skye, UK
- Data Source
  KAKENHI-PROJECT-18K03355
[Presentation] Dynamical degrees and singularity patterns2018
- Author(s)
  T. Mase, R. Willox, A. Ramani and B. Grammaticos
- Organizer
  Symmetries and Integrability of Difference Equations : SIDE13
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03355
[Presentation] 特異点閉じ込めと代数的エントロピー II2017
- Author(s)
  R. Willox, T. Mase, A. Ramani and B. Grammaticos
- Organizer
  非線形波動研究の新潮流 - 理論と応用 - 九州大学応用力学研究所，福岡
- Data Source
  KAKENHI-PROJECT-15K04893
[Presentation] From singularity patterns to algebraic entropies2017
- Author(s)
  Ralph Willox
- Organizer
  ISQS25, the XXVth International Conference on Integrable Systems and Quantum Symmetries, Prague, Czech Republic
- Data Source
  KAKENHI-PROJECT-15K04893
[Presentation] Ultradiscrete inverse scattering and an elementary linearization of the Takahashi-Satsuma box-ball system2016
- Author(s)
  Ralph Willox
- Organizer
  Classical and Quantum Integrability meeting
- Place of Presentation
  University of Glasgow, UK
- Year and Date
  2016-03-11
- Invited
- Data Source
  KAKENHI-PROJECT-15K04893
[Presentation] Singularity confinement 2.0 : an easily implementable and sufficient integrability criterion, at last ?2016
- Author(s)
  Ralph Willox
- Organizer
  2016 Joint Mathematics Meetings
- Place of Presentation
  Seattle, USA
- Year and Date
  2016-01-06
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893
[Presentation] Singularity confinement, anticonfinement and algebraic entropy2016
- Author(s)
  Ralph Willox
- Organizer
  AMS Fall Western Sectional Meeting
- Place of Presentation
  University of Denver, Denver, USA
- Year and Date
  2016-10-08
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893
[Presentation] Full-deautonomisation or how to obtain the algebraic entropy of a map from singularity confinement2016
- Author(s)
  Ralph Willox
- Organizer
  SIDE XII conference: Symmetries and Integrability of Difference Equations
- Place of Presentation
  Sainte-Adele, Quebec, Canada
- Year and Date
  2016-07-06
- Data Source
  KAKENHI-PROJECT-15K04893
[Presentation] A direct linearization of a Box & Ball system with arbitrary carrier capacity2016
- Author(s)
  Ralph Willox
- Organizer
  Discrete Integrable Systems Workshop 2016 at TSIMF
- Place of Presentation
  Sanya, China
- Year and Date
  2016-04-15
- Invited
- Data Source
  KAKENHI-PROJECT-15K04893
[Presentation] 箱玉系の線形化に対する初等的アプローチ2016
- Author(s)
  筧三郎, J.J.C. Nimmo, 辻本諭, R. Willox
- Organizer
  日本数学会2016年度年会
- Place of Presentation
  筑波大学（茨城県つくば市）
- Year and Date
  2016-03-19
- Data Source
  KAKENHI-PROJECT-23540252
[Presentation] Ultradiscrete inverse scattering and combinatorics2015
- Author(s)
  Ralph Willox and Saburo Kakei
- Organizer
  The 8th International Congress on Industrial and Applied Mathematics (ICIAM2015, Beijing, China)
- Place of Presentation
  北京（中国）
- Year and Date
  2015-08-11
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23540252
[Presentation] Ultradiscrete Inverse Scattering and Combinatorics2015
- Author(s)
  Ralph Willox
- Organizer
  ICIAM 2015
- Place of Presentation
  Beijing, China
- Year and Date
  2015-08-11
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K04893
[Presentation] Deautonomisation by singularity confinement: an algebro-geometric justification2014
- Author(s)
  Ralph Willox
- Organizer
  Integrable Systems 2014
- Place of Presentation
  The University of Sydney, Australia
- Year and Date
  2014-12-04
- Invited
- Data Source
  KAKENHI-PROJECT-24540204
[Presentation] The Hirota-Miwa equation, its integrability and its reductions2014
- Author(s)
  Ralph Willox
- Organizer
  DISCRETE INTEGRABLE SYSTEMS
- Place of Presentation
  NATIONAL MATHEMATICS INITIATIVE (NMI) Indian Institute of Science, Bangalore、インド
- Year and Date
  2014-06-14
- Invited
- Data Source
  KAKENHI-PROJECT-24540204
[Presentation] Modeling of natural phenomena through ultradiscretisation2014
- Author(s)
  Ralph Willox
- Organizer
  非線形数理モデルの諸相：連続，離散，超離散，その先
- Place of Presentation
  マス・フォア・インダストリ研究所・九州大学
- Year and Date
  2014-08-06
- Invited
- Data Source
  KAKENHI-PROJECT-24540204
[Presentation] Discretisations of constrained KP hierarchies2014
- Author(s)
  Ralph Willox
- Organizer
  SYMMETRIES & INTEGRABILITY IN DIFFERENCE EQUATIONS [SIDE - XI]
- Place of Presentation
  NATIONAL MATHEMATICS INITIATIVE (NMI) Indian Institute of Science, Bangalore、インド
- Year and Date
  2014-06-19
- Data Source
  KAKENHI-PROJECT-24540204
[Presentation] The ultradiscrete KdV equation defined over the real numbers2011
- Author(s)
  Ralph WILLOX
- Organizer
  Tropical Geometry and Integrable Systems
- Place of Presentation
  グラスゴー大学・連合王国(招待講演)
- Year and Date
  2011-07-05
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] The ultra discrete KdV equation defined over the real numbers2011
- Author(s)
  Ralph Willox
- Organizer
  Tropical Geometry and Integrable Systems
- Place of Presentation
  University of Glasgow,スコットランド
- Year and Date
  2011-07-05
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] 超離散KdV方程式の解法2010
- Author(s)
  Ralph WILLOX
- Organizer
  日本数学会・2010年度秋季総合分科会無限可積分系セッション・特別講演
- Place of Presentation
  名古屋大学大学院多元数理科学研究科
- Year and Date
  2010-09-24
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] Constructing ultra-discretisable Yang-Baxter maps2010
- Author(s)
  Ralph Willox
- Organizer
  China-Japan Joint Workshop on Integrable Systems
- Place of Presentation
  紹興市,中国
- Year and Date
  2010-01-07
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] 超離散KdV方程式の解法,無限可積分系セッション・特別講演2010
- Author(s)
  Ralph Willox
- Organizer
  日本数学会・秋季総合分科会
- Place of Presentation
  名古屋大学大学院多元数理科学研究科
- Year and Date
  2010-09-24
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] Solving the initial value problem for the ultradiscrete KdV equation2010
- Author(s)
  Ralph WILLOX
- Organizer
  Integrable Systems and Geometry, ICM 2010 Satellite Meeting
- Place of Presentation
  ポンディチェリ・インド
- Year and Date
  2010-08-16
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] Constructing ultradiscretisable Yang-Baxter maps2010
- Author(s)
  Ralph WILLOX
- Organizer
  China-Japan Joint Workshop on Integrable Systems
- Place of Presentation
  紹興市,中国
- Year and Date
  2010-01-07
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] Solving the initial value problem for the ultra discrete KdV equation, Integrable Systems and Geometry2010
- Author(s)
  Ralph Willox
- Organizer
  ICM 2010 Satellite Meeting
- Place of Presentation
  Pondicherry Uni-versity,インド
- Year and Date
  2010-08-16
- Data Source
  KAKENHI-PROJECT-21540210
[Presentation] Crystal-like structuresarising from the dKP hierarchy2009
- Author(s)
  R. Willox
- Organizer
  Geometric Aspects of Discrete andUltra-Discrete Integrable Systems
- Place of Presentation
  University ofGlasgow、スコットランド(連合王国)
- Year and Date
  2009-03-30
- Data Source
  KAKENHI-PROJECT-18540204
[Presentation] "Box and Ball"systems and Yang-Baxter maps2008
- Author(s)
  R. Willox, Discrete KP
- Organizer
  Nonlinear Waves - Theory and Applications
- Place of Presentation
  北京(中国)
- Year and Date
  2008-06-09
- Data Source
  KAKENHI-PROJECT-18540204
[Presentation] Construction of Yang-Baxter maps from the discrete Kphierar- chy2008
- Author(s)
  R. Willox
- Organizer
  Aspects of QuantumIntegrability
- Place of Presentation
  京都大学基礎物理学研究所
- Year and Date
  2008-07-24
- Data Source
  KAKENHI-PROJECT-18540204
[Presentation] Construction of Yang-Baxter maps from the discrete KP hierarchy2008
- Author(s)
  R. Willox
- Organizer
  Aspects of Quantum Integrability
- Place of Presentation
  京都大学
- Year and Date
  2008-07-24
- Data Source
  KAKENHI-PROJECT-18540204
[Presentation] Discrete KP, "Box and Ball" systems and Yang-Baxter maps2008
- Author(s)
  R. Willox
- Organizer
  Nonlinear Waves-Theory and Applications
- Place of Presentation
  北京(中国)
- Year and Date
  2008-06-09
- Data Source
  KAKENHI-PROJECT-18540204
[Presentation] Local Darboux transformations and geometrical crystals2007
- Author(s)
  R. Willox
- Organizer
  ISLAND3
- Place of Presentation
  Islay, UK
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16204009
[Presentation] Local Darboux transformationsand geometric crystals2007
- Author(s)
  R. Willox
- Organizer
  Alge-braic aspects of integrable systems
- Place of Presentation
  Islay、スコットランド(連合王国)
- Year and Date
  2007-07-02
- Data Source
  KAKENHI-PROJECT-18540204
[Presentation] 拡張されたTzitzeica方程式と中心等積アフィン曲面
- Author(s)
  三谷浩将，筧三郎，Ralph Willox
- Organizer
  共同利用研究集会「非線形波動研究の最前線 ―構造と現象の多様性―」
- Place of Presentation
  九州大学応用力学研究所
- Data Source
  KAKENHI-PROJECT-23540252
[Presentation] Ultradiscrete systems : integrable cellular automata and beyond
- Author(s)
  Ralph Willox
- Organizer
  JSPS-DST Asian Academic Seminar 2013 : Discrete Mathematics & its Applications
- Place of Presentation
  東京大学
- Invited
- Data Source
  KAKENHI-PROJECT-24540204
[Presentation] Solving the ultradiscrete KdV equation over the reals
- Author(s)
  Ralph WILLOX
- Organizer
  China-Japan Joint Workshop on Integrable Systems
- Place of Presentation
  京都大学
- Data Source
  KAKENHI-PROJECT-24540204
[Presentation] The ultradiscrete sine-Gordon equation and its exotic soliton interactions
- Author(s)
  Ralph Willox
- Organizer
  Nonlinear Mathematical Physics: Twenty Years of JNMP
- Place of Presentation
  The Sophus Lie Conference Center, Nordfjordeid（ノルウェー）
- Data Source
  KAKENHI-PROJECT-24540204
[Presentation] An IST-like solution to the Cauchy problem for a soliton cellular automaton
- Author(s)
  Ralph Willox
- Organizer
  2014 Joint Mathematics Meetings of the American Mathematical Society & the Mathematical Association of America
- Place of Presentation
  Baltimore（米国）
- Data Source
  KAKENHI-PROJECT-24540204
[Presentation] 超離散 sine-Gordon 方程式におけるソリトンの相互作用
- Author(s)
  Ralph Willox
- Organizer
  非線形波動研究の拡がり
- Place of Presentation
  九州大学
- Data Source
  KAKENHI-PROJECT-24540204

1. TOKIHIRO Tetsuji (10163966)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
2. OKAMOTO Kazuo (40011720)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
3. SAKAI Hidetaka (50323465)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
4. IZUMI Makoto (50263497)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
5. TAKENAWA Tomoyuki (70361805)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
6. INOUE Rei (30431901)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
7. JIMOBO Michio (80109082)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
8. SHIRAISHI Jun-ichi (20272536)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
9. NISHINARI Katsuhiro (40272083)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
10. SATSUMA Junkichi (70093242)

# of Collaborated Projects: 1 results

# of Collaborated Products: 1 results
11. KAKEI Saburo (60318798)

# of Collaborated Projects: 1 results

# of Collaborated Products: 5 results
12. SAITO Yoshihisa (20294522)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
13. Wada Youichiro (10322033)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
14. KATSURA Mari (30436571)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
15. ISHIZAKI Azusa (10558894)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
16. AKIMITSU Nobuyoshi (40294962)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
17. 國場敦夫 (70211886)

# of Collaborated Projects: 1 results

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18. 中村佳正 (50172458)

# of Collaborated Projects: 1 results

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19. STOKES ALEXANDER

# of Collaborated Projects: 1 results

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20. 間瀬崇史

# of Collaborated Projects: 0 results

# of Collaborated Products: 4 results

Willox Ralph ＷＩＬＬＯＸ Ｒａｌｐｈ

WILLOX Ralph ウィロックス ラルフ

RALPH WILLOX ラルフ ウイロツクス

Research Projects

Research Products

Co-Researchers

Extending the geometric theory of discrete Painleve equations - singularities, entropy and integrabilityPrincipal Investigator

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ntegrability of nonlinear partial difference and functional equations: a singularity and entropy based approachPrincipal Investigator

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Classification and characterization of the integrability of rational difference equations based on their dynamical degreePrincipal Investigator

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Algebraic and geometric properties of discrete integrable systemsPrincipal Investigator

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Evaluation of radiation effect based on point mutation of BRAF gene

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Towards a unified research method for ultradiscrete integrable systemsPrincipal Investigator

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Extension of special functions from the viewpoint of integrable systems

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Study on the integrable structure of ultradiscrete systems

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Direct methods for ultradiscrete systemsPrincipal Investigator

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Study of methods for analysing continuous systems, relying ondiscrete and ultra-discrete systemsPrincipal Investigator

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リダクションによるパンルヴェ方程式の研究Principal Investigator

Principal Investigator

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Mathematics on discrete and ultradiscrete integrable systems and its application

Principal Investigator

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[Book] Detecting discrete integrability: the singularity approach, in ``Nonlinear Systems and Their Remarkable Mathematical Structures: Volume I"2018

Author(s)

Willox Ralph ＷＩＬＬＯＸＲａｌｐｈ

WILLOX Ralph ウィロックスラルフ

RALPH WILLOX ラルフウイロツクス