Scholarlink

<p>We continue the study for standing wave solutions of <i>abcd</i>-systems which was started by Chen and Iooss (Chen, M., Iooss, G.: <i>Eur.&#xa0;J.&#xa0;Mech.&#xa0;B, Fluids</i>, 24(1):113–124, 2005) 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 <i>abcd</i>-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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Standing Wave Solutions of abcd-systems for Water Waves

  • 期刊论文

  • 发表日期：

    2026年4月11日

查看全文
  • Peifei Song,
  • Yuhao Xie,
  • Min Chen,
  • Shenghao Li

摘要

We continue the study for standing wave solutions of abcd-systems which was started by Chen and Iooss (Chen, M., Iooss, G.: Eur. J. Mech. B, Fluids, 24(1):113–124, 2005) 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.