Periodic and solitary traveling wave solutions for the generalized Kadomtsev-Petviashvili equation

This paper is concerned with traveling waves for the generalized Kadomtsev-Petviashvili equation (w(t) + w(xi xi xi) +f(w)(xi))(xi) = w(yy),(xi, y) is an element of R-2, t is an element of R, i.e. solutions of the form w(t, xi, y) = u(xi - ct, y). We study both, solutions periodic in x = xi - ct and solitary waves, which are decaying in x, and their interrelations. In particular, we prove the existence of a sequence of k-periodic solutions, k is an element of N, which is uniformly bounded in norm and converges to a solitary wave in a suitable topology. This result also holds for the corresponding ground states, i.e. solutions with minimal energy. Copyright (C) 1999 John Wiley & Sons, Ltd.