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

João Paulo Dias, Mário Figueira, Filipe Oliveira

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)547-564
Number of pages18
JournalProceedings Of The Royal Society Of Edinburgh Section A-Mathematics
Volume146
Issue number3
DOIs
Publication statusPublished - 2016

Keywords

  • dispersive equations
  • hyperbolic systems
  • linearized stability
  • long wave-short wave interactions
  • solitary waves

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