Soliton interactions of the Kadomtsev-Petviashvili equation and generation of large-amplitude water waves

TL;DR

This paper investigates how line-soliton interactions in the KPII equation can produce large water waves, providing a predictive method and numerical verification of the robustness of multi-soliton interactions and their wave amplitudes.

Contribution

It introduces a method to predict maximum wave amplitudes from asymptotic data and verifies the robustness of soliton interactions through numerical simulations.

Findings

Maximum wave amplitudes can be predicted from asymptotic data.

Multi-soliton interactions produce robust web-like structures.

Numerical simulations confirm the generation of large-amplitude water waves.

Abstract

We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of KPII. We also describe a method to predict the possible maximum wave amplitude from asymptotic data. Finally, we report on numerical simulations of multi-soliton complexes of the KPII equation which verify the robustness of all types of soliton interactions and web-like structure.