TY - JOUR
T1 - Transverse Instability of the CH-KP-I Equation
AU - Chen , Robin Ming
AU - Jin , Jie
JO - Annals of Applied Mathematics
VL - 3
SP - 337
EP - 362
PY - 2021
DA - 2021/09
SN - 37
DO - http://doi.org/10.4208/aam.OA-2021-0004
UR - https://global-sci.org/intro/article_detail/aam/19850.html
KW - Camassa-Holm-Kadomtsev-Ketviashvili-I equation, line solitary waves, transverse instability.
AB - <p style="text-align: justify;">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 [18]. 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.</p>