动力学和等离子体中(3+1)维Jimbo-Miwa方程丰富的精确解
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摘要
在符号计算软件Mathematica的帮助下,利用拓展后的变系数齐次平衡法,获得了动力学和等离子体中(3+1)维Jimbo-Miwa方程的新的自Bcklund变换。再利用获得的自Bcklund变换和Hirota双线性形式得到大量新的精确解。同时,通过给出一些三维图形展示了这些被获得的精确的物理性质和结构。
In this work,new auto-Bcklund transformation are obtained for the(3+1)-dimensional JimboMiwa equation by using the extended variable-coefficient homogeneous balance method(EvcHB)and symbolic computation.Abundant new exact solutions are derived by utilizing the new auto-Bcklund transformation and the simplified Hirota's method.The physical properties and structures of these obtained solutions are demonstrated by some plots.
In this work,new auto-Bcklund transformation are obtained for the(3+1)-dimensional JimboMiwa equation by using the extended variable-coefficient homogeneous balance method(EvcHB)and symbolic computation.Abundant new exact solutions are derived by utilizing the new auto-Bcklund transformation and the simplified Hirota's method.The physical properties and structures of these obtained solutions are demonstrated by some plots.
引文
[1]刘建国,曾志芳.变系数Sine-Gordon方程的Bcklund变换和新的精确解[J].系统科学与数学,2014,34(6):763-768.
[2]LIU J G,TIAB Y,ZENG Z F.New Exact Periodic Solitary-wave Solutions for the New(3+1)-dimensional Generalized Kadomtsev-Petviashvili Equation in Multi-temperature Electron Plasmas[J].AIP Adv,2017,7,105013.
[3]袁娜.(3+1)维Boiti-Leon-Manna-Pempinelli方程新的三波解[J].南昌大学学报(理科版),2017,41(4):319-323.
[4]傅海明,戴正德.(3+1)维孤子方程的周期孤波解[J].东北师大学报(自然科学版),2011,43(1):16-19.
[5]LIU J G,HE Y.New Periodic Solitary Wave Solutions for the(3+1)-dimensional Generalized Shallow Water Equation[J].Nonlinear Dynamics,2017,90(1):363-369.
[6]赵欢,邱震钰.(3+1)维破裂孤子方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(2):114-117.
[7]LIU J G,DU J Q,ZENG Z F,NIE B.New Three-wave Solutions for the(3+1)-dimensional Boiti–leon–manna–pempinelli Equation[J].Nonlinear Dynamics,2017,88(1):655-661.
[8]熊伟.(3+1)维Yu-Toda-Sasa-Fukuyama方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(3):211-215.
[9]付中华,李良树.(G'/G)展开法求解(3+1)维Jimbo-Miwa方程新的精确解[J].南昌大学学报(理科版),2017,41(05):418-422.
[10]蒋燕,刘建国.(3+1)维变系数Kadomtsev-Petviashvili方程的多孤子解[J].南昌大学学报(理科版),2014,38(6):527-529.
[11]万亮,龚雅玲,刘建国.广义Kuramoto-Sivashinsky方程的孤子解[J].南昌大学学报(理科版),2015,39(4):319-322.
[12]刘双,刘建国.忆阻器混沌振荡器的分支分析[J].南昌大学学报(理科版),2016,40(3):229-232.
[13]JIMBO M,MIWA T.Solitons and In-nite Dimensional Lie Algebra[J].Publ Res Inst Math Sci,1983,19:943-948.
[14]MA W X.A Transformed Rational Function Method and Exact Solutions to the(3+1)Dimensional Jimbo-Miwa Equation[J].Chaos Solitons Fractals,2009,42:1356-1363.
[15]ABDUL-MAJID W.Multiple-soliton Solutions for the Calogero-Bogoyavlenskii-Schiff,Jimbo-Miwa and YTSF Equations[J].Appl Math Comput,2008,203:592-597.
[16]TANG Y.Wronskian Determinant Solutions of the(3+1)-dimensional Jimbo-Miwa Equation[J].Appl Math Comput,2011,217:8722-8730.
[2]LIU J G,TIAB Y,ZENG Z F.New Exact Periodic Solitary-wave Solutions for the New(3+1)-dimensional Generalized Kadomtsev-Petviashvili Equation in Multi-temperature Electron Plasmas[J].AIP Adv,2017,7,105013.
[3]袁娜.(3+1)维Boiti-Leon-Manna-Pempinelli方程新的三波解[J].南昌大学学报(理科版),2017,41(4):319-323.
[4]傅海明,戴正德.(3+1)维孤子方程的周期孤波解[J].东北师大学报(自然科学版),2011,43(1):16-19.
[5]LIU J G,HE Y.New Periodic Solitary Wave Solutions for the(3+1)-dimensional Generalized Shallow Water Equation[J].Nonlinear Dynamics,2017,90(1):363-369.
[6]赵欢,邱震钰.(3+1)维破裂孤子方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(2):114-117.
[7]LIU J G,DU J Q,ZENG Z F,NIE B.New Three-wave Solutions for the(3+1)-dimensional Boiti–leon–manna–pempinelli Equation[J].Nonlinear Dynamics,2017,88(1):655-661.
[8]熊伟.(3+1)维Yu-Toda-Sasa-Fukuyama方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(3):211-215.
[9]付中华,李良树.(G'/G)展开法求解(3+1)维Jimbo-Miwa方程新的精确解[J].南昌大学学报(理科版),2017,41(05):418-422.
[10]蒋燕,刘建国.(3+1)维变系数Kadomtsev-Petviashvili方程的多孤子解[J].南昌大学学报(理科版),2014,38(6):527-529.
[11]万亮,龚雅玲,刘建国.广义Kuramoto-Sivashinsky方程的孤子解[J].南昌大学学报(理科版),2015,39(4):319-322.
[12]刘双,刘建国.忆阻器混沌振荡器的分支分析[J].南昌大学学报(理科版),2016,40(3):229-232.
[13]JIMBO M,MIWA T.Solitons and In-nite Dimensional Lie Algebra[J].Publ Res Inst Math Sci,1983,19:943-948.
[14]MA W X.A Transformed Rational Function Method and Exact Solutions to the(3+1)Dimensional Jimbo-Miwa Equation[J].Chaos Solitons Fractals,2009,42:1356-1363.
[15]ABDUL-MAJID W.Multiple-soliton Solutions for the Calogero-Bogoyavlenskii-Schiff,Jimbo-Miwa and YTSF Equations[J].Appl Math Comput,2008,203:592-597.
[16]TANG Y.Wronskian Determinant Solutions of the(3+1)-dimensional Jimbo-Miwa Equation[J].Appl Math Comput,2011,217:8722-8730.