时间分数阶Camassa-Holm型方程的各种精确解及其动力学性质
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摘要
利用变量分离法与齐次平衡原理相结合的方法,系统地研究了时间分数阶Camassa-Holm型方程,获得该方程各种类型的精确解,并讨论了这些解的稳定性、有界性、渐进性等动力学性质和衰减现象,通过图像模拟,以图例的形式直观地展示了部分精确解的动力学行为和动力学现象.
The time fractional Camassa-Holm equation is systematically studied by using the method of variable separation combined with homogeneous balance principle. And the stability,boundedness,asymptotic properties and decay of these solutions are discussed. Through image simulation,the dynamic behavior and dynamic phenomena of some exact solutions are displayed intuitively in the form of legend.
The time fractional Camassa-Holm equation is systematically studied by using the method of variable separation combined with homogeneous balance principle. And the stability,boundedness,asymptotic properties and decay of these solutions are discussed. Through image simulation,the dynamic behavior and dynamic phenomena of some exact solutions are displayed intuitively in the form of legend.
引文
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[17]黄潇,芮伟国.分数阶广义Bagley-Torvik方程的各种精确解及其动力学性质[J].云南大学学报(自然科学版),2018,40(1):12-21.
[2]ESLAMI M,VAJARGAH B F,MIRZAZADEH M,et al.Applications of first integral Method to fractional partial differential equations[J].Indian Journal of Physics,2014,88(2):177-184.
[3]BAKKYARAJ T,SAHADEVAN R.Approximate analytical solution of two coupled time fractional nonlinear Schrodinger equations[J].International Journal of Applied and Computational Mathematics,2016,2(1):113-135.
[4]SAHADEVAN R,BAKKYARAJ T.Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations[J].Journal of Mathematical Analysis and Applications,2012,393(2):341-347.
[5]SAHADEVAN R,BAKKYARAJ T.Invariant subspace method and exact solutions of certain nonlinear time fractional partial differential equations[J].Fractional Calculus and Applied Analysis,2015,18(1):146-162.
[6]HARRIS P A,GARRA R.Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method[J].Nonlinear Studies,2013,20(4):471-481.
[7]WU G,LEE E W M.Fractional variational iteration method and its application[J].Physics Letters A,2010,374(25):2506-2509.
[8]ELSAYED M E Z,YASSER A A,REHAM M A S.The fractional complex transformation for nonlinear fractional partial differential equations in the mathematical physics[J].Journal of Association of Arab Universities for Basic and Applied Sciences,2016,19:59-69.
[9]CHEN J,LIU F,ANH V.Analytical solution for the time-fractional telegraph equation by the method of separating variables[J].Journal of Mathematical A-nalysis and Applications,2008,338(2):1364-1377.
[10]RUI W.Applications of homogenous balanced principle on investigating exact solutions to a series of time fractional nonlinear PDEs[J].Communications in Nonlinear Science and Numerical Simulation,2017,47:253-266.
[11]RUI W.Applications of integral bifurcation method together with homogeneous balanced principle on investigating exact solutions of time fractional nonlinear PDEs[J].Nonlinear Dynamics,2018,91(1):697-712.
[12]GUI G,LIU Y.Global well-posedness and blow-up of solutions for the Camassa-Holm equations with fractional dissipation[J].Mathematische Zeitschrift,2015,281(3-4):993-1020.
[13]LIU ZHENGGRONG,GUO BOLING.Periodic blow-up solutions and their limit forms for the generalized Camassa-Holm equation[J].Progress in Natural Science,2008,18(3):259-266.
[14]ZHANG Y.Time-Fractional Camassa-Holm Equation:Formulation and Solution Using Variational Methods[J].Journal of Computational&Nonlinear Dynamics,2013,8(4):041020.
[15]刘刚,胡卫敏,张稳根.非线性分数阶微分方程边值问题多重正解的存在性[J].云南大学学报(自然科学版),2012,34(3):258-264.
[16]汤小松.一类分数阶微分方程三点边值问题正解的存在性和多重性[J].云南大学学报(自然科学版),2012,34(4):385-392.
[17]黄潇,芮伟国.分数阶广义Bagley-Torvik方程的各种精确解及其动力学性质[J].云南大学学报(自然科学版),2018,40(1):12-21.