Existence and concentration of nontrivial solitary waves for a generalized Kadomtsev--Petviashvili equation in $\mathbb{R}^2$

TL;DR

This paper investigates the existence and concentration phenomena of solitary waves in a generalized Kadomtsev-Petviashvili equation in two-dimensional space using variational techniques.

Contribution

It establishes the existence and concentration results for solitary waves in a generalized KP equation with potential, expanding understanding of wave behavior in such systems.

Findings

Existence of nontrivial solitary wave solutions.

Concentration behavior of solutions around potential minima.

Application of variational methods to a generalized KP equation.

Abstract

In this paper, we study the existence and concentration of solitary waves for a class of generalized Kadomtsev-Petviashvili equations with the potential in $\mathbb{R}^2$ via the variational methods.