中文摘要：

根据简化齐次平衡原则,导出一个由线性方程的解到一个具变耗散系数的柱Burgers方程解的非线性变换.该线性方程容许有指数函数形式的解,因而借助所导出的非线性变换,获得一个具变耗散系数的柱Burgers方程的精确解.完全类似地,也获得一个具变耗散系数的球Burgers方程的精确解.

英文摘要：

Based on the simplified homogeneous balance principle, a nonlinear transformation that forms the solution of a linear equation to the solution of a cylindrical Burgers equation with variable dissipative coefficient has been derived. Since the linear equation admits an exponential type solution,substituting it into the nonlinear transformation derived here, we have had the exact solution of the cylindrical Burgers equation with variable dissipative coefficient. This method can be used to obtain the exact solution of a spherical Burgers equation with variable dissipative coefficient too.