Water-wave gap solitons: An approximate theory and accurate numerical experiments

TL;DR

This paper develops an approximate coupled-mode theory for gravity water wave gap solitons in periodic topography, validated by numerical experiments showing long-lived localized wave groups and extending to three dimensions.

Contribution

It introduces a standard coupled-mode theoretical framework for water wave gap solitons and demonstrates its accuracy through numerical validation, including for strongly nonlinear waves and 3D extensions.

Findings

Coupled-mode theory accurately describes weakly-nonlinear water wave gap solitons.

Numerical simulations show long-lived, nearly standing localized water wave groups.

The model is extended to three-dimensional cases.

Abstract

It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this theory are in a reasonable agreement with accurate numerical simulations of exact equations of motion for ideal planar potential free-surface flows, even for strongly nonlinear waves. In numerical experiments, self-localized groups of nearly standing water waves can exist up to hundreds of wave periods. Generalizations of the model to the three-dimensional case are also derived.