A plethora of fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation

TL;DR

This paper demonstrates that the full-dispersion Kadomtsev-Petviashvili I (FDKP-I) equation admits a family of fully localized solitary waves, extending known solutions of the classical KP-I equation by perturbative methods.

Contribution

It establishes the existence of fully localized solitary waves for the FDKP-I equation using perturbation techniques and the implicit-function theorem.

Findings

Existence of symmetric fully localized solitary waves for FDKP-I

Extension of KP-I solitary wave solutions to the full-dispersion model

Application of implicit-function theorem in a novel perturbative context

Abstract

The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with Bond number $\beta>1/3$, also called strong surface tension. This equation has recently been shown to have a family of nondegenerate, symmetric `fully localised' or `lump' solitary waves which decay to zero in all spatial directions. The full-dispersion KP-I equation is obtained by retaining the exact dispersion relation in the modelling from the water-wave problem. In this paper we show that the FDKP-I equation also has a family of symmetric fullly localised solitary waves which are obtained by casting it as a perturbation of the KP-I equation and applying a suitable variant of the implicit-function theorem.