A Few Integrable Dynamical Systems,Recurrence Operators,Expanding Integrable Models and Hamiltonian Structures by the r-Matrix Method  

作　　者：张玉峰 Iqbal Muhammad 岳超 

机构地区：[1]College of Mathematics, China University of Mining and Technology [2]College of Medical Information Engineering, Taishan Medical University

出　　处：《Communications in Theoretical Physics》2017年第10期463-470,共8页理论物理通讯（英文版）

基　　金：Supported by the Fundamental Research Funds for the Central University under Grant No.2017XKZD11

摘　　要：We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov-Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the （29-1）-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of （29-1）-dimensional expanding dynamical model of the （29-1）-dimensionaJ dynamical system is generated as well.

关 键 词：R-MATRIX poisson tensor expanding dynamical system 

分 类 号：O19[理学—数学]