用算符法求解物理学非线性微分方程

Solving the Nonlinear Differential Equations in Physics by Means of Operator

引入特征算符和相应的算符定理,用算符法把物理学中的非线性微分方程的叠代解表示成展开的幂级数,结合辅助函数,得出所要求的级数解,提供一种用算符法求解物理学非线性微分方程的技巧.

This paper introduces the characteristic operator and its corresponding theorem, obtains the required series solution by indicating the iteratives solutions of the non-linear differential equations in Physics as unfolded power series with operator and combination with auxiliary functions. It also provides a skill of solving the non-linear differential equations in Physics by means of operator.