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arXiv · 2307.12821

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

Anna Geyer·Yue Liu·Dmitry E. Pelinovsky
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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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Anna Geyer, Yue Liu, Dmitry E. Pelinovsky. 2023-07-24. On the transverse stability of smooth solitary waves in a two-dimensional Camassa-Holm equation. https://arxiv.org/abs/2307.12821

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