Standing waves for a two-way model system for water waves
In this paper, we prove the existence of a large
family of non-trivial bifurcating standing waves for a model system which descri
bes
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 2 parameters representing the
time-period and the wave length, and the average of one of the amplitudes.
Min Chen (chen@math.purdue.edu)