Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

TL;DR

This paper conducts a detailed numerical analysis of the Kadomtsev-Petviashvili (KP) equation, focusing on the small dispersion limit and oscillatory regimes, to address gaps in analytical understanding and compare with related models.

Contribution

It provides the first comprehensive numerical investigation of the small dispersion limit of the KP equation, including regimes with large amplitudes and transverse effects.

Findings

Identified oscillatory behaviors in the small dispersion limit.

Compared KP oscillatory regimes with KdV dynamics.

Explored the influence of the transverse coordinate on the limit.

Abstract

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.