  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.
