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

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.