Quasi-linearization and stability analysis of some self-dual,dark equations and a new dynamical system  

作　　者：Denis Blackmore Mykola M Prytula Anatolij K Prykarpatski 

机构地区：[1]Department of Mathematical Sciences and CAMS,New Jersey Institute of Technology,Newark NJ 07102 United States of America [2]Ivan Franko National University of Lviv,Ukraine [3]Cracow University of Technology,Cracow,Poland

出　　处：《Communications in Theoretical Physics》2022年第10期60-67,共8页理论物理通讯（英文版）

摘　　要：We describe a class of self-dual dark nonlinear dynamical systems a priori allowing their quasilinearization,whose integrability can be effectively studied by means of a geometrically based gradient-holonomic approach.A special case of the self-dual dynamical system,parametrically dependent on a functional variable is considered,and the related integrability condition is formulated.Using this integrability scheme,we study a new self-dual,dark nonlinear dynamical system on a smooth functional manifold,which models the interaction of atmospheric magnetosonic Alfvén plasma waves.We prove that this dynamical system possesses a Lax representation that allows its full direct linearization and compatible Poisson structures.Moreover,for this selfdual nonlinear dynamical system we construct an infinite hierarchy of mutually commuting conservation laws and prove its complete integrability.

关 键 词：Hamiltonian system Poisson structure conservation laws dark evolution system asymptotic analysis complete integrability 

分 类 号：O175[理学—数学]