On existence theorems of periodic traveling wave solution to the generalized forced Kadomtsev-Petviashvili equation

Abstract

This paper is concerned with periodic traveling wave solutions of the generalized forced Kadomtsev-Petviashvili equation in the form ( u_t +[f(u)]_x + α u_xxx )_x + β u_yy = h₀. The basic approach to this problem is to establish an equivalence relationship between a periodic boundary value problem and nonlinear integral equations with symmetric kernels by using the Green's function method. The integral representations generate compact operators in a Banach space of real-valued continuous periodic functions with a given period 2T. Schauder's fixed point theorem is then used to prove the existence of nonconstant periodic traveling wave solutions.