Communications in Mathematical Analysis

Periodic Travelling Waves and its Inter-relation with Solitons for the 2D abc-Boussinesq System

Jose R. Quintero and Alex M. Montes

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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.

Article information

Commun. Math. Anal., Volume 20, Number 1 (2017), 27-49.

First available in Project Euclid: 17 May 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics 35B10: Periodic solutions 35Q51: Soliton-like equations [See also 37K40] 35A15: Variational methods

Periodic travelling waves solitary waves Concentration-compactness principle variational principle


Quintero, Jose R.; Montes, Alex M. Periodic Travelling Waves and its Inter-relation with Solitons for the 2D abc-Boussinesq System. Commun. Math. Anal. 20 (2017), no. 1, 27--49.

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