Does solitary wave solution persist for the long wave equation with small perturbations?
Analysis of PDEs
2022-10-03 v1 Classical Analysis and ODEs
Abstract
In this paper, persistence of solitary wave solutions of the regularized long wave equation with small perturbations are investigated by the geometric singular perturbation theory. Two different kinds of the perturbations are considered in this paper: one is the weak backward diffusion and dissipation, the other is the Marangoni effects. Indeed, the solitary wave persists under small perturbations. Furthermore, the different perturbations do affect the proper wave speed ensuring the persistence of the solitary waves. Finally, numerical simulations are utilized to confirm the theoretical results.
Keywords
Cite
@article{arxiv.2209.15636,
title = {Does solitary wave solution persist for the long wave equation with small perturbations?},
author = {Hang Zheng and Y-H. Xia},
journal= {arXiv preprint arXiv:2209.15636},
year = {2022}
}