A host of traveling waves in a model of three-dimensional water-wave dynamics
Abstract
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an infinite-dimensional family. We characterize these solutions through spatial dynamics, by reducing a linearly ill-posed mixed-type initial-value problem to a center manifold of infinite dimension and codimension. A unique global solution exists for arbitrary small initial data for the two-component bottom velocity, specified along a single line in the direction of translation (or orthogonal to it). A dispersive, nonlocal, nonlinear wave equation governs the spatial evolution of bottom velocity.
Keywords
Cite
@article{arxiv.nlin/0111045,
title = {A host of traveling waves in a model of three-dimensional water-wave dynamics},
author = {Robert L. Pego and Jose Raul Quintero},
journal= {arXiv preprint arXiv:nlin/0111045},
year = {2015}
}
Comments
22 pages with 1 figure, LaTeX2e with amsfonts, epsfig packages