On the transverse stability of smooth solitary waves in a two-dimensional Camassa–Holm equation

Journal article (2024)

Authors

A. Geyer Mathematical Physics - EEMCS
Yue Liu University of Texas at Arlington
Dmitry E. Pelinovsky McMaster University, Nizhny Novgorod State Technical University
Research Group
Mathematical Physics (EEMCS) (TU Delft)
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Published Date

2024

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

We consider the propagation of smooth solitary waves in a two-dimensional generalization of the Camassa–Holm equation. We show that transverse perturbations to one-dimensional solitary waves behave similarly to the KP-II theory. This conclusion follows from our two main results: (i) the double eigenvalue of the linearized equations related to the translational symmetry breaks under a transverse perturbation into a pair of the asymptotically stable resonances and (ii) small-amplitude solitary waves are linearly stable with respect to transverse perturbations.

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