Nontrivial solitary waves to the generalized Kadomtsev–Petviashvili equations

摘要

In this note, we study the existence of nontrivial solitary waves for the generalized Kadomtsev–Petviashvili equation in multi-dimensional spaces. Our main tool is a recent linking theorem stated in a paper by Szulkin and Zou [A. Szulkin, W. Zou, Homoclinic orbit for asymptotically linear Hamiltonian systems, J. Funct. Anal. 187 (2001) 25–41].