Contents Online
Methods and Applications of Analysis
Volume 21 (2014)
Number 2
From periodic travelling waves to solitons of a 2D water wave system
Pages: 241 – 264
DOI: https://dx.doi.org/10.4310/MAA.2014.v21.n2.a4
Author
Abstract
We use a variational approach to establish the existence of $x$-periodic travelling waves and its interrelation with solitons for a 2D water wave system for three-dimensional water wave dynamics in the weakly nonlinear long-wave regime. As common in many 1D water wave models, we show that a special sequence of the $x$-periodic 2D travelling wave solutions parametrized by the period $k$ is uniformly bounded in norm and converges to a soliton in $\mathbb{R}^2$ (solitary wave of finite energy) in an appropriate sense, indicating that the shape of $x$-periodic 2D travelling waves of period $k$ and solitons are almost the same, as the period $k$ is big enough.
Keywords
2D Boussinesq water wave system, Periodic travelling waves, solitons, variational methods
2010 Mathematics Subject Classification
35A15, 35B10, 35Q35, 37K40
Published 13 August 2014