Orbital Stability Of A Sum Of Solitons And Breathers Of The Modified Korteweg-de Vries Equation

2021/10/29 by A. Semenov, Semenov, Alexander
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2110.15617

openalex publication_date 2021/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove that a sum of solitons and breathers of the modified Korteweg-de Vries equation (mKdV) is orbitally stable. The orbital stability is shown in H². More precisely, we will show that if a solution of (mKdV) is close enough to a sum of solitons and breathers with distinct velocities at t=0 in the H² sense, then it stays close to this sum of solitons and breathers, up to space translations for solitons and space or phase translations for breathers. From this, we deduce the orbital stability of a multi-breather of (mKdV), constructed in [49]. As an application of the orbital stability and the formula for multi-breathers obtained by inverse scattering method [51], we deduce a result about uniqueness of multi-breathers.

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