English

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

R2 v1 2026-06-23T18:21:54.908Z