变换理论求解非线性常微分方程的若干进展

Most of the problems involved in nature are nonlinear, and the existing approximate analytic theory of nonlinear system can not accurately explain the nature of its complex phenomena, so the exact solution of nonlinear system has very important significance. In this paper, the research progress of analytical solutions of nonlinear ordinary differential equations by using transformation theory is summarized. Firstly, the transformation process of nonlinear ordinary differential equations with arbitrary parameters and their analytical solutions are reviewed. Secondly, the transformation process of nonlinear ordinary differential equations with integrable parameters and their corresponding analytic solutions are reviewed. Finally, some suggestions for the study of exact analytical solutions for nonlinear systems are given.