A New Non-Isospectral Integrable Hierarchy and Some Associated Symmetries  

作　　者：Yufeng ZHANG Yiyi LIU Jian-gen LIU Binlu FENG 

机构地区：[1]School of Mathematics and Information Sciences,Weifang University,Shandong 261061,P.R.China [2]College of Mathematics,China University of Mining and Technology,Jiangsu 221116,P.R.China [3]School of Mathematics and Statistics,Changshu Institute of Technology,Jiangsu 215500,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第5期573-596,共24页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 11971475;12371256)。

摘　　要：By applying a subgroup of the Lie group Mn C we introduce a linear nonisospectral problem whose compatibility condition gives rise to a nonisospectral integrable hierarchy of evolution equations, which reduces to a generalized nonisospectral integrable hierarchy(GNIH).The GNIH further reduces to the standard nonlinear Schr¨odinger equation and the Kd V equation which have important applications in physics science. Based on this, we discuss the K symmetries and the τ symmetries of the generalized AKNS hierarchy u_t = K_m(u) with isospectral condition coming from the GNIH. Furthermore, we also consider the K symmetries and the τ symmetries of the nonisospectral AKNS hierarchy ut = τ_N~l +1. Finally, we obtain the symmetry Lie algebras for the both integrable hierarchies, and present some applications for the symmetries and the Lie algebras, which means that some Lie groups of transformations and the infinitesimal operators of reduced equations are generated.

关 键 词：integrable hierarchy SYMMETRY non-isospectral hierarchy 

分 类 号：O152.5[理学—数学]