Standing waves for a two-way model system for water waves

Min Chen (1) , Gérard Iooss (2)

1 Department of Mathematics
2 INLN - Institut Non Linéaire de Nice Sophia-Antipolis

In this paper, we prove the existence of a large family of nontrivial bifurcating standing waves for a model system which describes two-way propagation of water waves in a channel of finite depth or in the near shore zone. In particular, it is shown that, contrary to the classical standing gravity wave problem on a fluid layer of finite depth, the Lyapunov–Schmidt method applies to find the bifurcation equation. The bifurcation set is formed with the discrete union of Whitney's umbrellas in the three-dimensional space formed with 3 parameters representing the time-period and the wave length, and the average of wave amplitude.

Mots clés: standing waves; water waves

Domaines: Systèmes dynamiques [math.DS]

Min Chen, Gérard Iooss. Standing waves for a two-way model system for water waves. European Journal of Mechanics - B/Fluids, 2005, 24, pp.113-124. ⟨10.1016/j.euromechflu.2004.07.002⟩. ⟨hal-00014170⟩