Degasperis-Procesi方程的类孤子新解

利用辅助方程与函数变换相结合的方法,构造了Degasperis-Procesi(D-P)方程的无穷序列类孤子新解.首先,通过两种函数变换,把D-P方程化为常微分方程组.然后,利用常微分方程组的首次积分,把D-P方程的求解问题化为几种常微分方程的求解问题.最后,利用几种常微分方程的Bcklund变换等相关结论,构造了D-P方程的无穷序列类孤子新解.这里包括由Riemannθ函数、Jacobi椭圆函数、双曲函数、三角函数和有理函数组成的无穷序列光滑孤立子解、尖峰孤立子解和紧孤立子解.

New Soliton-like Solutions of Degasperis-Procesi Equation

The method for combing the auxiliary equation with the function transformations is presented to search for new infinite sequence soliton-like solutions of Degasperis-Procesi(D-P) equation.Firstly,two function transformations are applied to change D-P equation into a set of ordinary differential equations.Then the problem of solving the solutions of D-P equation is transformed into the problem of solving the solutions of several normal ordinary differential equations according to the first integral of the set of the ordinary differential equations.Finally,new infinite sequence soliton-like solutions of D-P equation are constructed by using Backlund transformation of the several ordinary differential equations and other relative conclusions.The solutions include infinite sequence smooth soliton solutions,peak soliton solutions and compact soliton solutions composed of Riemann θ function,Jacobi elliptic function,hyperbolic function,trigonometric function and rational function.