Standing wave solutions of $abcd$-systems for water waves
Analysis of PDEs
2025-07-02 v1
Abstract
We continue the study for standing wave solutions of -systems which was started by Chen and Iooss \cite{chen2005standing} for the BBM system via the Lyapunov-Schmidt method. In this paper, we will first discuss the feasibility of the Lyapunov-Schmidt method for bifurcating standing wave solutions of -systems. These systems will be characterized into three categories: feasible, infeasible and uncertain feasible ones. In particular, we prove the existence of nontrivial bifurcating standing waves for the Bona-Smith system.
Cite
@article{arxiv.2507.00436,
title = {Standing wave solutions of $abcd$-systems for water waves},
author = {Peifei Song and Yuhao Xie and Min Chen and Shenghao Li},
journal= {arXiv preprint arXiv:2507.00436},
year = {2025}
}