Solitary waves for a class of generalized Kadomtsev-Petviashvili equation in $\mathbb{R}^N$ with positive and zero mass

TL;DR

This paper employs variational methods to establish existence results for solitary waves in a generalized Kadomtsev-Petviashvili equation across various dimensions, considering both positive and zero mass scenarios.

Contribution

It extends the Berestycki-Lions framework to a class of generalized KP equations in multiple dimensions, addressing both positive and zero mass cases.

Findings

Existence of solitary wave solutions established.

Application of variational methods to generalized KP equations.

Results cover multiple spatial dimensions.

Abstract

In this paper we use variational methods to establish a Berestycki-Lions type result for a class of generalized Kadomtsev-Petviashvili equation in $\mathbb{R}^N$. The positive and zero mass cases are considered.