Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-27T02:52:09.598Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence and linearized stability of solitary waves for a quasilinear Benney system

Part of: Representations of solutions General higher-order equations and systems

Published online by Cambridge University Press:  21 March 2016

João-Paulo Dias ,
Mário Figueira  and
Filipe Oliveira
João-Paulo Dias
Affiliation:
CMAF-UL, Av. Prof. Gama Pinto, 1649-003 Lisboa, Portugal and DM-FCUL, Campo Grande, 1749-016 Lisboa, Portugal ([email protected]; [email protected])
Mário Figueira
Affiliation:
CMAF-UL, Av. Prof. Gama Pinto, 1649-003 Lisboa, Portugal and DM-FCUL, Campo Grande, 1749-016 Lisboa, Portugal ([email protected]; [email protected])
Filipe Oliveira
Affiliation:
CMAF-UL, Av. Prof. Gama Pinto, 1649-003 Lisboa, Portugal and FCT-UNL, Monte da Caparica, 2829-516 Caparica, Portugal ([email protected])
Get access Rights & Permissions [Opens in a new window]

Extract

We prove the existence of solitary wave solutions to the quasilinear Benney system

where , –1 < p < +∞ and a, γ > 0. We establish, in particular, the existence of travelling waves with speed arbitrarily large if p < 0 and arbitrarily close to 0 if . We also show the existence of standing waves in the case , with compact support if – 1 < p < 0. Finally, we obtain, under certain conditions, the linearized stability of such solutions.

Keywords

long wave–short wave interactionssolitary wavesdispersive equationshyperbolic systemslinearized stability

MSC classification

Secondary: 35G55: Initial value problems for nonlinear higher-order systems 35C07: Traveling wave solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 3 , June 2016 , pp. 547 - 564
Copyright
Copyright © Royal Society of Edinburgh 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)