Three New(2+1)-dimensional Integrable Systems and Some Related Darboux Transformations  

作　　者：郭秀荣 

机构地区：[1]Basic Courses, Shandong University of Science and Technology

出　　处：《Communications in Theoretical Physics》2016年第6期735-742,共8页理论物理通讯（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant No.11371361;the Shandong Provincial Natural Science Foundation of China under Grant Nos.ZR2012AQ011,ZR2013AL016,ZR2015EM042;National Social Science Foundation of China under Grant No.13BJY026;the Development of Science and Technology Project under Grant No.2015NS1048;A Project of Shandong Province Higher Educational Science and Technology Program under Grant No.J14LI58

摘　　要：We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1,then under the framework of zero curvature equations we generate two(2+1)-dimensional integrable hierarchies, including the(2+1)-dimensional shallow water wave(SWW) hierarchy and the(2+1)-dimensional Kaup–Newell(KN)hierarchy. Through reduction of the(2+1)-dimensional hierarchies, we get a(2+1)-dimensional SWW equation and a(2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the(2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the(2+1)-dimensional KN equation could be deduced. Finally,with the help of the spatial spectral matrix of SWW hierarchy, we generate a(2+1) heat equation and a(2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang–Mills equations.

关 键 词：（2＋1）-dimensional equation Lie algebra Darboux transformation 

分 类 号：O175.5[理学—数学]