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

Abstract

This paper is concerned with traveling waves for the generalized Kadomtsev-Petviashvili equation (w t +w ξξξ +f(w) ξ ) ξ =w yy , (ξ,y) ∈ R 2 , t∈ R, i.e. solutions of the form w(t,ξ,y) = u(ξ - et, y). We study both. solutions periodic in x = ξ - 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 ∈ 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.