符号计算与AKNS孤子方程族的自动推导

Symbolic Computation and Automatic Deriving of AKNS Soliton Equation Hierarchy

讨论由Ｌａｘ 对得到的ＡＫＮＳ孤子方程族，求得Ｌａｘ 对对应的Ｌｅｎａｒｄ 递推方程的显式解，进而利用符号计算技术自动推导出显式孤子方程族，并给出用Ｍａｔｈｅｍａｔｉｃａ 数学软件编写的符号计算程序．

This paper studies the AKNS soliton hierarchy derived from its Lax pair.The explicit solutions to the Lenard's equation corresponding to the Lax pair are obtained.The technology of symbolic computation is applied to derive automatically the soliton hicrarchy of explicit form.In the end,the program of symbolic computation written in Mathematica language is presented.