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| Transverse Instability of the CH-KP-I Equation |
| Robin Ming Chen,Jie Jin |
| (Department of Mathematics, University of Pittsburgh, Pittsburgh PA 15260,
USA) |
| DOI： |
| 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 [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. |
| Key words: Camassa-Holm-Kadomtsev-Ketviashvili-I equation, line solitary waves, trans verse instability |