拟线性波方程的函数分离变量解

Functional separable solutions to quasi-linear wave equations

利用群分叶法研究了带有变速度和外力项的拟线性波方程u_(tt)=(A(x)D(u)u_x^n)_x+Q(u)的函数变量分离问题.对于允许和型或乘积型分离变量解的二阶波方程给出了一个完整的分类.

Functional separation of variables for the quasi-linear wave equations with a variable wave speed and external force term utt = （A（x）D（u）ux^n~）x＋ Q（u） was studied in terms of the group foliation method. A classification was carried out for the second order wave equations which admit additive or product separable solutions.