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

Published online by Cambridge University Press:  21 March 2016

João-Paulo Dias
Affiliation:
CMAF-UL, Av. Prof. Gama Pinto, 1649-003 Lisboa, Portugal and DM-FCUL, Campo Grande, 1749-016 Lisboa, Portugal (dias@ptmat.fc.ul.pt; figueira@ptmat.fc.ul.pt)
Mário Figueira
Affiliation:
CMAF-UL, Av. Prof. Gama Pinto, 1649-003 Lisboa, Portugal and DM-FCUL, Campo Grande, 1749-016 Lisboa, Portugal (dias@ptmat.fc.ul.pt; figueira@ptmat.fc.ul.pt)
Filipe Oliveira
Affiliation:
CMAF-UL, Av. Prof. Gama Pinto, 1649-003 Lisboa, Portugal and FCT-UNL, Monte da Caparica, 2829-516 Caparica, Portugal (fso@fct.unl.pt)

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2016 

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