Solitary gravity-capillary water waves with point vortices

TL;DR

This paper constructs small-amplitude solitary gravity-capillary water waves with point vortices, analyzing how vortex positions influence wave properties, using a bifurcation approach on finite depth water.

Contribution

It introduces a novel bifurcation method to construct solitary waves with point vortices in finite depth water, highlighting the impact of vortex placement.

Findings

Wave properties depend on vortex positions

Successful construction of small-amplitude solitary waves with vortices

Analysis of vortex influence on wave characteristics

Abstract

We construct small-amplitude solitary traveling gravity-capillary water waves with a finite number of point vortices along a vertical line, on finite depth. This is done using a local bifurcation argument. The properties of the resulting waves are also examined: We find that they depend significantly on the position of the point vortices in the water column.