非保谱AKNS族的对易表示

Reciprocal Representation of Variable Spectral AKNS Hierachy

给出一个直接从李群结构方程出发构造发展方程和相应的对易表示的方法。并以此方法为框架应用到AKNS族，建立了非保谱AKNS族的对易表示（含保谱的情形），并将讼参数ξ关于时间的演化关系扩大到，后种情形在以前的文章中还未出现过。作为特例，得到了Sine-Gordon方程族及相应的对易表示。

In this paper, a method is given to construct evolution equation and reciprocalrepresentation resorting to the structure equation of Lie Groups. To use this method forAKNS hierachy, the reciprocal representation of variable spectral AKNS hierachy (includinginvariable spectral) are obtained, and this method expands the dependent relation of the spectral and time upto from . In particular, thereciprocal representation of the Sine-Gordon equation hierachy are obtained.