## Communications in Mathematical Analysis

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 17 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.cma/1494986415

Mathematical Reviews number (MathSciNet)
MR3645766

Zentralblatt MATH identifier
1372.35247

#### Citation

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. https://projecteuclid.org/euclid.cma/1494986415