K(m,n)方程与B(m,n)方程的无穷序列新精确解

Infinite sequence new exact solutions of K(m,n) equation and B(m,n) equation

进一步研究了辅助方程法,给出了几种常用辅助方程的新解、B(a|¨)cklund变换和解的非线性叠加公式.在此基础上,根据m和n的不同情况,利用变换和直接积分相结合的方法,获得了K(m,n)方程与B(m,n)方程的无穷序列新精确解.这里包括无穷序列光滑孤立子解、无穷序列尖峰孤立子解和无穷序列紧孤立子解.

New solutions of several kinds of auxiliary equations, Backlund transformation and nonlinear superposition formula of the solu- tions are presented by studying a highly auxiliary equation method. Based on this and different m and n, the method of combining transformation and direct integration is used to obtain infinite sequence new exact solutions of K （m, n） equation and B （m, n） equa- tion, which include infinite sequence smooth soliton solutions, peak soliton solutions and compact soliton solutions.