Existence of two-dimensional deep capillary solitary water waves with constant vorticity

Abstract

We consider two-dimensional capillary water waves with nonzero constant vorticity in infinite depth. We first derive the Babenko equation that describes the profile of the solitary wave. When the velocity $c$ is close to a critical velocity, the Babenko equation can be reduced to the stationary focusing cubic nonlinear Schrödinger equation plus perturbative error. This gives the existence of small-amplitude solitary wave solutions for the water wave system with constant vorticity whose profiles are close to solutions of the stationary focusing cubic nonlinear Schrödinger equation.

arXiv comment30 pages, title changed