标度变换与变系数非线性发展方程的精确解

Scaling Transformations and Exact Solutions for Several Nonlinear Evolution Equations with Variable Coefficients

将Cariello和Tabor提出的求解不可积非线性发展方程精确解的方法推广到变系数方程的情形,并通过求解奇异流形函数的约束方程组和由标度变换引出的相似约化方程给出了变系数Burgers方程,变系数KdV-Burgers方程,变系数Newell-Whitehead方程的精确解.

The method to solve non-integrable nonlinear evolution equations given by Cariello and Tabor is generalized to the case of variable coefficient equations. The exact solutions for the variable coefficient Burgers equation, KdV-Burgers equation and Newell-Whitehead equation are presented through solving the restricted equations of singular manifold functions and the similarity reduction equations induced from the scaling transformation.