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.
作者
毛辉
张孟霞
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)
出处
《应用数学学报》
CSCD
北大核心
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
