The Boussinesq systems on the background of a line solitary wave

Hung Luong; Jean-Claude Saut

doi:10.3934/dcds.2022179

Article Contents

2023, Volume 43, Issue 5: 1787-1823. Doi: 10.3934/dcds.2022179

This issue Previous Article Linear non-degeneracy and uniqueness of the bubble solution for the critical fractional Hénon equation in $ \mathbb{R}^N $ Next Article Long-time behavior of solutions to the $ M_1 $ model with boundary effect

The Boussinesq systems on the background of a line solitary wave

Hung Luong^1, and
Jean-Claude Saut^2,

1.
Institute of Mathematics, VAST, 18B Hoang Quoc Viet street, Cau Giay, Hanoi, Viet Nam
2.
Laboratoire de Mathématiques, UMR 8628, Université Paris-Saclay et CNRS, 91405 Orsay, France

Received: May 2022

Early access: December 2022

Published: May 2023

¹The first author is supported by International Centre of Research and Postgraduate Training in Mathematics (ICRTM) under grant number ICRTM04-2021.02.
²The second author was partially supported by the ANR Project AnuI (ANR-17-CE40-0035- 02)

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Abstract

This paper is motivated by the transverse stability properties of the line solitary wave solutions of the (a, b, c, d) class of Boussinesq systems introduced in [15,18]. We first review the known results on existence of one-dimensional solitary waves. Then we address the question of long time existence of the systems satisfied by a localized perturbation of a line solitary wave.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35Q55.

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