Two types of new algorithms for finding explicit analytical solutions of nonlinear differential equations

The idea of AC=BD was applied to solve the nonlinear differential equations. Suppose that Au=0 is a given equation to be solved and Dv=0 is an equation to be easily solved. If the transformation u=Cv is obtained so that v satisfies Dv=0, then the solutions for Au=0 can be found. In order to illustrate this approach, several examples about the transformation C are given. Paper from ZHANG Hong-qing, Member of Editorial Commitee, AMM Foundation item: the National Basic Research Program Foundation of China (G1998030600); Doctoral Foundation of Education Commitee of China (98014119) Biography: ZHANG Hong-qing (1936-)