两个(2+1)-维超对称可积系统的B?cklund变换和Lax对  

On Two (2+1)-dimensional Supersymmetric Integrable Systems:Backlund Transformations and Lax Pairs

作　　者：毛辉 张孟霞[2] MAO HUI;ZHANG MENGXIA(School of Mathematics and Statistics,Nanning Normal University,Nanning 530001;Department of Mathematics,China University of Mining and Technology,Beijing 100083)

机构地区：[1]南宁师范大学数学与统计学院,南宁530001 [2]中国矿业大学(北京)理学院,北京100083

出　　处：《应用数学学报》2019年第5期712-720,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11905110,11871471,11401572,11271366,11331008);广西自然科学基金(No.2018GXNSFBA050020);广西高校中青年教师基础能力提升项目(No.2019KY0417);南宁师范大学科研启动项目(No.0819-2018L13)资助

摘　　要：本文考虑了最近出现的两个(2+1)-维超对称可积系统,它们分别被称为超对称负Kadomtsev-Petviashvili(KP)以及超对称(2+1)-维修正Korteweg-de Vries(mKdV).我们构造了它们的Backlund变换和Lax对以及一类精确解,从而进一步确定了它们的可积性.It is observed that most studies on supersymmetric integrable systems are in(1+1)-dimensions.However,higher dimensional integrable systems such as KadomtsevPetviashvili equation and Davey-Stewartson equation are also important in mathematics and physics.Thus,it is worthwhile to supersymmetrize higher dimensional integrable equations and examine their properties.Two recently proposed(2+1)-dimensional supersymmetric systems,namely supersymmetric negative Kadomtsev-Petviashvili(NKP)and supersymmetric(2+1)-dimensional modified Korteweg-de Vries(MKdV)are considered.Through the Hirota’s bilinear method,their Backlund transformations and Lax representations are constructed and some solutions are calculated for them.Backlund transformations and Lax representations are important in the study of nonlinear systems.On the one hand,they may be adopted to construct solutions for the corresponding nonlinear systems.On the other hand,they may be applied to generate new integrable systems,both continuous and discrete.Since most integrable systems have Backlund transformation and Lax representation,the existence of them may also be taken as a criterion for integrability.So in this way the integrability of these two systems is confirmed.

关 键 词：BACKLUND变换 LAX对 Hirota直接方法 超对称 

分 类 号：O175.24[理学—数学]