A plethora of generalised solitary gravity-capillary water waves

TL;DR

This paper introduces an efficient numerical algorithm for computing generalized solitary gravity-capillary water waves and provides evidence for the existence of infinitely many such waves with oscillatory wings.

Contribution

It develops a conformal mapping-based numerical method to solve Babenko-like equations for generalized solitary waves in water.

Findings

Numerical solutions for a wide class of solitary waves with oscillatory wings.

Evidence supporting the existence of infinitely many generalized solitary waves.

An efficient computational approach for gravity-capillary wave analysis.

Abstract

The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an infinite number of generalised solitary waves (solitary waves with undamped oscillatory wings). Using conformal mapping, the unknown fluid domain, which is to be determined, is mapped into a uniform strip of the complex plane. In the transformed domain, a Babenko-like equation is then derived and solved numerically.