一个非线性波方程的李对称与精确解

摘要

To study a nonlinear wave equation,the Lie symmetry analysis method and the bifurcation theory of dynamical system are used to obtain the symmetries of the equation and the exact parametric representations of traveling wave solutions with the aid of Maple,and the phase portraits of traveling wave system are given.The simulation results show that the Lie symmetry analysis is a effective mathematical tool for study nonlinear evolution equations.%为研究一个非线性波方程,借助符号计算软件 Maple,采用李对称分析并结合动力系统理论的分支方法,得到该方程的李点对称和行波解的精确参数表达式,并给出了行波系统的相图。结果表明,李对称分析对于研究非线性发展方程是一个有效的数学工具。