In this paper we study the generalized 2D-BO equation in two dimensions: . All righ .ir ðut þ bHuxx þ uuxÞx þ uyy 1⁄4 0; ðx; yÞ 2 R; t P 0: We classify the existence and non-existence of solitary waves depending on the sign of , b and on the nonlinearity. We also prove nonlinear stability and some regularity properties of such waves. 2011 Elsevier Inc. All… (More)