带自相容源KdV、mKdV和Harry Dym方程之间的Backlund变换-《集美大学学报（自然科学版）》

文章信息/Info

Title:: Backlund Transformations Between KdV Equation and mKdV Equation with Self-consistent Sources,mKdV Equation and Harry Dym Equation with Self-consistent Sources

Author(s):: GAO Liangjuan1; WU Hongxia1; ZENG Yunbo2; (1.School of Science,Jimei University,Xiamen 361021,China；2.Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China)

Keywords:: KdV equation with sources; modified KdV equation with sources; Harry Dym equation with sources; Backlund transformation

摘要:: 在Sato理论的框架下，利用拟微分算子探讨了1+1维带源可积方程族之间的Backlund 变换，构造了带源KdV 方程与带源 mKdV 方程、带源 mKdV 方程和带源 Harry Dym 方程之间的 Backlund 变换，结果表明，在所构造的Backlund 变换作用下，第一（二）型标准的带源KdV、mKdV方程分别变换成非标准的第一（二）型的带源mKdV、Harry Dym方程。

Abstract:: Backlund transformations between 1+1 dimensional integrable hierarchies by the pseudo-differential operator in the framework of Sato theory are discussed.Backlund transformation between KdV equation with self-consistent sources(with sources) and mKdV equation with sources,mKdV equation with sources and Harry Dym equation with sources are given,respectively.The results show that under the Backlund transformation,the first(two) standard type of KdV,mKdV equation with sources are transformed into the first(two) non-standard type of mKdV,Harry Dym equation with sources,respectively.