【摘要】 利用已建立的Lie代数构造了一类新的含复数的谱问题,再用一个不含谱参数的规范变换将该谱问题转化为著名的Zakharov-Shabat特征值问题,由此得到了新的位势函数与原来的位势函数间的代数运算关系,也就是说,如果取原来函数的某些特殊值作为种子解的话,则利用该规范变换就可得到新的精确解.最后,将该规范变换约化为非线性演化方程的达布变换.更多还原

【Abstract】 By using the known Lie algebras,a type of new spectral problem containing complex number is constructed,which turns to well-known Zakharov-Shabat eigenvalue problem by employing a gauge transformation without spectral parameter.It follows that the relations between new potential functions and the orginal ones are linked up.That is,if we get some special values of the orginal potential functions as seed solutions,then we could obtain new solutions on potential functions.Finally,the guage transformation obtained in this paper reduces to a Darboux transformation of nonlinear evolution equations.更多还原