Remarks on the bifurcation of two-dimensional capillary-gravity waves of finite depth
Summary: We determine two-dimensional water waves of permanent configuration. This problem is a bifurcation problem. We define a mapping \(G\) between two Hilbert spaces and prove that the solutions of the above problem are in one-to-one correspondence to the zeros of the mapping \(G\). Our most important contribution is to clarify the role of the aspect ratio , i.e., the ratio between the mean depth of the flow and the wave length. In particular, we prove that there is no degenerate bifurcation point, whatever the aspect ratio may be.
scientific article; zbMATH DE number 741435
scientific article