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2017 Periodic Travelling Waves and its Inter-relation with Solitons for the 2D abc-Boussinesq System
Jose R. Quintero, Alex M. Montes
Commun. Math. Anal. 20(1): 27-49 (2017).

Abstract

Via a variational approach involving Concentration-Compactness principle, we show the existence of $x$-periodic travelling wave solutions for a general 2D-Boussinesq system that arises in the study of the evolution of long water waves with small amplitude in the presence of surface tension. We also establish that $x$-periodic travelling waves have almost the same shape of solitons as the period tends to infinity, by showing that a special sequence of $x$-periodic travelling wave solutions parameterized by the period converges to a solitary wave in a appropriate sense.

Citation

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Jose R. Quintero. Alex M. Montes. "Periodic Travelling Waves and its Inter-relation with Solitons for the 2D abc-Boussinesq System." Commun. Math. Anal. 20 (1) 27 - 49, 2017.

Information

Published: 2017
First available in Project Euclid: 17 May 2017

zbMATH: 1372.35247
MathSciNet: MR3645766

Subjects:
Primary: 35A15, 35B10, 35Q35, 35Q51

Rights: Copyright © 2017 Mathematical Research Publishers

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Vol.20 • No. 1 • 2017
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