摘要
本文给出求解ＫｄＶ方程的一种代数方法．利用这种方法可以得到ＫｄＶ方程的３－参数解族和４－参数解族的解析显式．证明了由反散射变换（ＩＳＴ）得到的孤立子解是这里给出的多参数解族的特例．经适当的约化和双曲函数的恒等变形，由这些多参数解族可得经Ｂａｃｋｌｕｎｄ变换产生的多孤子解．
In this paper,the three parameter and four parameter solution family of the KdV equation are given by means of an algebraic method.It is shown that the well known soliton solutions of the KdV equation obtained by using the method of the inverse scattering transformation (IST) are the special cases of these multiple parameter solution family.By some proper reduction,the multiple soliton solutions of the KdV equation generated by Backlund transformation could be obtained from the expressions in the paper.
基金
国家自然科学基金
浙江省自然科学基金
