On the existence and analycity of solitary waves solutions to a two-dimesional Benjamin-Ono equation

Abstract

We show the existence, regularity and analyticity of solitary waves associated to the following equation \begin{eqnarray*} (u_t+u^{p}u_x+ \mathcal H\partial_x^2u+ \lambda \mathcal H\partial_y^2u)_x +\mu u_{yy}=0, \end{eqnarray*} where $\mathcal H$ is the Hilbert transform with respect to $x$ and $\lambda$ and $\mu$ are nonnegative real numbers, not simultaneously zero.