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arXiv · 2307.09932

Linear stability of elastic 2-line solitons for the KP-II equation

Tetsu Mizumachi
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Abstract

The KP-II equation was derived by Kadomtsev and Petviashvili to explain stability of line solitary waves of shallow water. Using the Darboux transformations, we study linear stability of 2-line solitons whose line solitons interact elastically each other. Time evolution of resonant continuous eigenfunctions is described by a damped wave equation in the transverse variable which is supposed to be a linear approximation of the local phase shifts of modulating line solitons.

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Tetsu Mizumachi. 2023-07-19. Linear stability of elastic 2-line solitons for the KP-II equation. https://arxiv.org/abs/2307.09932

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