寻找变系数非线性方程精确解的新方法

A NEW METHOD TO SOLVE NONLINEAR VARIABLE COEFFICIENT EQUATION

将非线性方程的变系数看作与实际物理场具有相等地位的新变量,利用普遍的经典李群方法可以求解某些特殊类型的变系数方程,其解由相应的常系数方程的解表示.以非线性薛定谔方程为具体例子,介绍了这种方法.并给出了特例色散缓变光纤变系数非线性薛定谔方程的精确解.

Starting from symmetry properties of equation and considering the variable coefficient of the equation as a new dependent variable,a new general method to solve variable coefficient equation is proposed.The solution of variable coefficient equation can be expressed by an arbitrary solution of the corresponding constant coefficient equation.Taking Schrdinger equation as a concrete example,the method is recommended in detail.