On exact travelling wave solutions for two types of nonlinear K (n, n) equations and a generalized KP equation

Abstract

In this paper, we study two types of genuinely nonlinear K (n, n) equations and a generalized KP equation. By developing a mathematical method based on the reduction of order of nonlinear differential equations, we derive general formulas for the travelling wave solutions of the three equations. The compactons, solitary patterns, solitons and periodic solutions obtained are expressed analytically. It is shown that the y and z components of the wave number vectors in the travelling wave solutions of the generalized KP equation remain free and arbitrary constants. The work generalizes the known results of travelling wave solutions for the three equations. © 2007 Elsevier B.V. All rights reserved.