亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

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

        2022-11-10 12:15:08DenisBlackmoreMykolaPrytulaandAnatolijPrykarpatski
        Communications in Theoretical Physics 2022年10期

        Denis Blackmore,Mykola M Prytula and Anatolij K Prykarpatski

        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

        Abstract 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.

        Keywords:Hamiltonian system,Poisson structure,conservation laws,dark evolution system,asymptotic analysis,complete integrability

        1.Introduction

        Some twenty years ago,a new class of nonlinear dynamical systems,called ‘dark equations’ was introduced by Boris Kupershmidt[1,2],and shown to possess unusual properties that were not particularly well-understood at that time.Later,in related developments,some Burgers-type[3–5]and also Korteweg–de Vries type[6,7]dynamical systems were studied in detail,and it was proved that they have a finite number of conservation laws,a linearization and degenerate Lax representations,among other properties.In what follows,we provide a description of a class of self-dual dark-type(or just,dark,for short)nonlinear dynamical systems,which a priori allows their quasi-linearization,whose integrability can be effectively studied by means of a geometrically motivated[8,9–11]gradient-holonomic approach[12–14].Moreover,we study a slightly modified form of a self-dual nonlinear dark dynamical system on a functional manifold,whose integrability was recently analyzed in[15].Not only did this dynamical system appear to be Lax integrable,it also seemed to have a rich mathematical architecture including compatible Poisson structures and an infinite hierarchy of nontrivial mutually commuting conservation laws.In the sequel,we shall prove these properties using the gradient-holonomic integrability scheme devised in our prior work with several collaborators[12–14].

        The remainder of this investigation is organized as follows.In section 2,we describe a rather wide class of self-dual dark quasi-linearized nonlinear dynamical systems on smooth functional manifolds.Then,in section 3,we study their quasilinearization property along with the integrability of a new selfdual nonlinear dark dynamical system.Next,in section 4,we prove the existence of a bi-Hamiltonian structure for the new system,and deduce its complete integrability.Finally,section 5 is devoted to summarizing our results and indicating some possible related future research directions.

        2.Self-dual symmetry,quasi-linearization and nonlinear dark dynamical systems

        We begin by studying integrability properties of a certain class of nonlinear dynamical systems of the form

        3.Integrability description of dark equations

        3.1.Integrability analysis

        To proceed with the problem of classifying integrable dark dynamical systems on the functional manifold M,we need from the very beginning to analyze the conditions under which the reduced quasi-linearized system(2.3)possesses an infinite hierarchy of suitably ordered conservation laws.To do this,we will make use of the geometrically motivated gradient-holonomic integrability scheme devised in[16]and further developed in[12–14],to first transform the vector fields(2.3)to their following equivalent form on the functional manifold:

        3.2.A new degenerate integrable dark type dynamical system

        4.Bi-Hamiltonian structure and complete integrability

        on the manifold Mu,whose solutions possess already much more nontrivial properties,and can suitably fit for modeling some physically interesting phenomena.

        Remark 4.4.It is worth mentioning here that the self-dual dynamical system(3.17)as well as those(4.14)constructed above,are not contained within the usual Burgers type hierarchy,which can be easily checked by making use of the analysis done before in[4,7].

        It is worth mentioning here that the integrability technique and results obtained above for the self-dual nonlinear dynamical system(3.17)on the functional manifold Mucan be effectively used via the corresponding Bogoyavlensky–Novikov reduction scheme[12–14,34]to describe a wide class of its both solitonic and finite-zoned quasiperiodic solutions in exact analytic form,which is now a topic of a work in progress.

        5.Concluding remarks

        We analyzed a new self-dual nonlinear dark dynamical system(on a functional manifold),which is a mathematical model of the interaction of atmospheric magneto-sonic Alfvén plasma waves.Using a gradient-holonomic approach,we were able to prove that the dynamical system is a completely integrable bi-Hamiltonian system,possessing an infinite hierarchy of nontrivial mutually commuting conservation laws with respect to the corresponding pair of compatible Poisson structures.It was noted that the gradient-holonomic approach,introduced by some of us and our collaborators,together with Bogoyavlensky–Novikov reduction,can apparently be used to construct a wide class of both solitonic and finite-zoned quasiperiodic solutions of the dark system in exact analytic form,and this is a goal that we are currently pursuing.

        Acknowledgments

        The authors are sincerely indebted to the Referees for their remarks and useful suggestions,which contributed to improving the manuscript.Especially AKP and MMP thank their colleagues D Dutych,Y Prykarpatsky and R Kycia for valuable discussions of computer-assisted calculational aspects related to the gradient-holonomic integrability approach.

        ORCID iDs

        av男人操美女一区二区三区| 一本大道久久a久久综合| 国产一区二区三区视频免费在线 | 综合无码综合网站| 狼人狠狠干首页综合网| 国偷自拍av一区二区三区| 国产裸体xxxx视频在线播放| 亚洲一区视频在线| 亚洲黑寡妇黄色一级片| 97人妻人人揉人人躁九色| 熟女人妇交换俱乐部| 精品不卡久久久久久无码人妻| 青青草绿色华人播放在线视频| 伊人久久大香线蕉av波多野结衣| 日产精品久久久久久久性色| 亚洲精品成人网线在线播放va| 亚洲av熟女传媒国产一区二区| 亚洲国产精品无码久久久| 国精产品一区二区三区| 亚洲日韩国产精品不卡一区在线| 精品一级一片内射播放| 久久综合九色综合97欧美| 特黄aa级毛片免费视频播放| 天堂av一区二区在线| 欧洲美女黑人粗性暴交视频| 少女高清影视在线观看动漫| 久久精品国产只有精品96| 在线日本国产成人免费精品| 亚洲乱亚洲乱妇50p| 亚洲手机国产精品| 午夜一区二区三区在线观看| 久久不见久久见免费视频6 | 中文字幕有码高清| 开心久久综合婷婷九月| 久久精品国产久精国产| 亚州无线国产2021| 蜜桃噜噜一区二区三区| 成人精品视频一区二区| 国产啪精品视频网给免丝袜| 日韩一区二区中文字幕视频| 国产极品粉嫩福利姬萌白酱|