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arXiv · 2507.00436

Standing wave solutions of $abcd$-systems for water waves

Peifei Song·Yuhao Xie·Min Chen·Shenghao Li
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Abstract

We continue the study for standing wave solutions of $abcd$-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 $abcd$-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.

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Peifei Song, Yuhao Xie, Min Chen, Shenghao Li. 2025-07-01. Standing wave solutions of $abcd$-systems for water waves. https://arxiv.org/abs/2507.00436

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