Existence, regularity and concentration phenomenon of nontrivial solitary waves for a class of Generalized Kadomtsev-Petviashvili (GKP) equation in $\mathbb{R}^2$

TL;DR

This paper investigates the existence, regularity, and concentration of solitary wave solutions for a generalized Kadomtsev-Petviashvili equation in two dimensions, using variational methods and anisotropic Sobolev spaces.

Contribution

It provides new results on the existence and concentration phenomena of solitary waves for GKP equations, addressing regularity in anisotropic Sobolev spaces.

Findings

Existence of nontrivial solitary waves established.

Concentration phenomena of solutions analyzed.

Regularity results in anisotropic Sobolev spaces obtained.

Abstract

In this paper we establish some results concerning the existence, regularity and concentration phenomenon of nontrivial solitary waves for a Generalized Kadomtsev-Petviashvili (GKP) equation in $\mathbb{R}^2.$ Variational methods are used to get an existence result and to study the concentration phenomenon, while the regularity is more delicate because we are leading with functions in an anisotropic Sobolev space.