Collision of water wave solitons

TL;DR

This paper classifies how water wave solitons interact over time, revealing different behaviors depending on their directions and number of wave extrema, with implications for understanding nonlinear wave dynamics.

Contribution

It provides a novel classification of two-soliton interactions in the Boussinesq equation based on extrema, distinguishing scenarios for same and opposite directions.

Findings

Three interaction scenarios for same-direction solitons.

Single scenario for opposite-direction solitons.

Insights into wave extrema during soliton collisions.

Abstract

A classification of the time evolution of the two-soliton solutions of the Boussinesq equation is given, based on the number of extrema of the wave. For solitons moving in the same directions, three different scenarios are found, while it is shown that only one of these scenarios exists in case of oppositely moving solitons.