Degasperis-Procesi方程的无穷序列尖峰孤立波解

摘要

本文为了构造非线性发展方程的无穷序列尖峰精确解，给出了Riccati方程的Backlund变换和解的非线性叠加公式，并借助符号计算系统Mathematica，用Degasperis-Procesi方程为应用实例，构造了无穷序列尖峰孤立波解和无穷序列尖峰周期解．%To construct infinite sequence peak solitary wave solutions to nonlinear evolution equations, Baicklund transformation of Riccati equation and nonlinear superposition formula of the solutions are introduced, then Degasperis - Procesi equation is taken as an example and infinite sequence peak solitary wave solutions and periodic solutions of the equation are obtained with the help of symbolic computation system Mathematica.