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

2023/07/19 by Tetsu Mizumachi, Mizumachi, Tetsu · 1 citation
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #35B35 #35Q35 #37K40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #Primary #Secondary

paper · pdf · doi:10.48550/arxiv.2307.09932

openalex publication_date 2023/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Transverse linear stability of line solitons for 2D Toda

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