Higher-dimensional integrable deformations of the modified KdV equation  

作　　者：Xiazhi Hao S Y Lou 

机构地区：[1]College of Science,Zhejiang University of Technology,Hangzhou,China [2]School of Physical Science and Technology,Ningbo University,Ningbo,315211,China

出　　处：《Communications in Theoretical Physics》2023年第7期15-21,共7页理论物理通讯（英文版）

基　　金：sponsored by the National Natural Science Foundations of China(Nos.12235007,11975131,11435005,12275144,11975204);KC Wong Magna Fund in Ningbo University;Natural Science Foundation of Zhejiang Province No.LQ20A010009。

摘　　要：The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability.The well-known modified Kd V equation is a prototypical example of an integrable evolution equation in one spatial dimension.Do there exist integrable analogs of the modified Kd V equation in higher spatial dimensions?In what follows,we present a positive answer to this question.In particular,rewriting the(1+1)-dimensional integrable modified Kd V equation in conservation forms and adding deformation mappings during the process allows one to construct higher-dimensional integrable equations.Further,we illustrate this idea with examples from the modified Kd V hierarchy and also present the Lax pairs of these higher-dimensional integrable evolution equations.

关 键 词：higher-dimensional integrable equation conservation form deformation mapping Lax integrability symmetry integrability 

分 类 号：O411.1[理学—理论物理]