中文摘要：

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.

英文摘要：

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 equa- tions. Finally, new infinite sequence soliton-like solutions of D-P equation are constructed by using B~icklund 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 ~ function, Jacobi elliptic function, hyperbolic function, trigonometric function and rational function.