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Stability of the line soliton of the KP-II equation under periodic transverse perturbations

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Abstract

We prove the nonlinear stability of the KdV solitary waves considered as solutions of the KP-II equation, with respect to periodic transverse perturbations. Our proof uses a Miura transform which sends the solutions of an mKP-II equation to solutions of the KP-II equation.

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Correspondence to Nikolay Tzvetkov.

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Mizumachi, T., Tzvetkov, N. Stability of the line soliton of the KP-II equation under periodic transverse perturbations. Math. Ann. 352, 659–690 (2012). https://doi.org/10.1007/s00208-011-0654-3

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  • DOI: https://doi.org/10.1007/s00208-011-0654-3

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