Remarks on solitary waves of the generalized two dimensional Benjamin–Ono equation

In this paper we study the generalized 2D-BO equation in two dimensions:(ut+βHuxx+upux)x+ϵuyy=0,(x,y)∈R2,t⩾0.We classify the existence and non-existence of solitary waves depending on the sign of ϵ, β and on the nonlinearity. We also prove nonlinear stability and some regularity properties of such waves.