Solitary wave interaction in a compact equation for deep-water gravity waves

TL;DR

This paper numerically investigates solitary wave solutions of a compact Zakharov equation for deep-water waves, revealing elastic collisions that suggest the equation's integrability.

Contribution

It provides the first numerical evidence of elastic solitary wave collisions in a compact deep-water wave model, indicating potential integrability.

Findings

Solitary waves are found to collide elastically.

The spectral scheme accurately computes wave solutions.

Results suggest the Zakharov equation may be integrable.

Abstract

In this study we compute numerical traveling wave solutions to a compact version of the Zakharov equation for unidirectional deep-water waves recently derived by Dyachenko & Zakharov (2011) Furthermore, by means of an accurate Fourier-type spectral scheme we find that solitary waves appear to collide elastically, suggesting the integrability of the Zakharov equation.