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arXiv · 2104.10825

Transverse instability of the CH-KP-I equation

Robin Ming Chen·Jie Jin
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Abstract

The Camassa-Holm-Kadomtsev-Petviashvili-I equation (CH-KP-I) is a two dimensional generalization of the Camassa-Holm equation (CH). In this paper, we prove transverse instability of the line solitary waves under periodic transverse perturbations. The proof is based on the framework of the paper written by Rousset and Tzvetkov. Due to the high nonlinearity, our proof requires necessary modification. Specifically, we first establish the linear instability of the line solitary waves. Then through an approximation procedure, we prove that the linear effect actually dominates the nonlinear behavior.

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Robin Ming Chen, Jie Jin. 2021-04-22. Transverse instability of the CH-KP-I equation. https://arxiv.org/abs/2104.10825

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