New bifurcation diagrams in the problem of permanent progressive waves

Abstract

Plane progressive waves on water of finite or infinite depth are treated under the effect of both gravity and surface tension. We are interested In the bifurcation phenomena, particularly in Wilton's waves which are obtained as a consequence of bifurcation of multiplicity two. We obtain bifurcating solutions and their bifurcation diagrams numerically. We include into solutions those waves in which the flow regions have self-intersections. By this, we see qualitative agreement of the numerical results with the mathematical theory.