Traveling Waves for the Nonlinear Variational Wave Equation
Analysis of PDEs
2022-01-13 v3
Abstract
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and constant segments, glued together at points where at least one one-sided derivative is unbounded. Applying the method of proof to the Camassa--Holm equation, we recover some well-known results on its traveling wave solutions.
Keywords
Cite
@article{arxiv.2009.03178,
title = {Traveling Waves for the Nonlinear Variational Wave Equation},
author = {Katrin Grunert and Audun Reigstad},
journal= {arXiv preprint arXiv:2009.03178},
year = {2022}
}
Comments
18 pages, 6 figures