河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
中国科技核心期刊
中国期刊方阵入选期刊
中国高校优秀科技期刊
华北优秀期刊
河北省优秀科技期刊

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五阶非线性发展方程的对称约化、精确解和守恒律

张和伟¹

刘庆松²

1. 枣庄科技职业学院计算机部, 山东枣庄 277500;
2. 聊城大学学报编辑部, 山东聊城 252059
DOI： 10.13763/j.cnki.jhebnu.nse.2017.04.001

Symmetry Reduction,Exact Solutions and Conservation Laws of a Fifth-order Nonlinear Equation

ZHANG Hewei¹, LIU Qingsong²

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摘要/Abstract

摘要：

利用李群方法，得到了五阶非线性发展方程的经典李对称、李代数和相似约化.利用幂级数方法得到了该方程的一系列精确幂级数解.最后由相应的李对称得到了该方程的守恒律.

Abstract：

By applying the Lie group method,we realize the classical Lie symmetry,Lie algebra and similarity reductions of a fifth-order nonlinear integrable equation.Employing power series method,we obtain the exact power series solutions.We also obtain conservation laws of the equation with the corresponding Lie symmetry.

关键词

关键词： 五阶非线性发展方程 ; 李群方法 ; 对称约化 ; 精确解 ; 幂级数方法 ; 守恒律

Key words： fifth-order nonlinear integrable equation ; Lie group method ; symmetry a reduction ; exact solutions ; power series method ; conservation laws

参考文献 25

[1] CHEN M,LIU X Q.Symmetries and Exact Solutions of the Breaking Soliton Equation[J].Communications in Theoretical Physics,2011,56:851-855.doi:10.1088/0253-6102.56.5.11
[2] TIAN Y H,CHEN H L,LIU X Q.A Simple Direct Method to Find Equivalence Transformations of a Generalized Nonlinear Schrodinger Equation and a Generalized KdV Equation[J].Applied Mathematics and Computation,2010,215:3509-3514.doi:10.1016/j.amc.2009.10.046
[3] ZHANG L H,LIU X Q.New Exact Solutions and Conservation Laws to (3+1)-dimensional Potential-YTSF Equation[J].Communications in Theoretical Physics,2006,45:487-492.doi:10.1088/0253-6102.45.3.022
[4] YAN Z L,LIU X Q,WANG L.The Direct Symmetry Method and Its Application in Variable Coefficients Schrodinger Equation[J].Applied Mathematics and Computation,2007,187:701-707.doi:10.1016/j.amc.2006.08.084
[5] YAN Z L,LIU X Q,YU X J.Classification and Similarity Solutions of Variable Coefficients Burgers Equation[J].Journal of Atomic and Molecular Physics,2007,24:1239-1244.
[6] YAN Z L,ZHOU J P.New Explicit Solutions of (1+1)-dimensional Variable-coefficient Broer-Kaup System[J].Communications in Theoretical Physics,2010,54:965-970.
[7] LOU S Y,MA H C.Non-Lie Symmetry Groups of (2+1)-dimensional Nonlinear Systems Obtained from a Simple Direct Method[J].Journal of Physics A:Mathematical and General,2005,38:129-137.doi:10.1088/0305-4470.38.7.L04
[8] XIN X P,LIU X Q,ZHANG L L.Explicit Solutions of the Bogoyavlensky Konoplechenko Equation[J].Applied Mathematics and Computation,2010,215:3669-3673.doi:10.1016/j.amc.2009.11.005
[9] SALAS A H.Exact Solutions for the General Fifth KdV Equation by the Exp Function Method[J].Applied Mathematics and Computation,2008,205:291-297.doi:10.1016/j.amc.2008.07.013
[10] ABLOWITZ M J,CLAKSON P A.Solutions,Nonlinear Evolution Equations and Inverse Scattering[M].Cambridge:Cambridge University Press,1991.doi:10.1016/0167-2789(86)90183.1
[11] LU D C,HONG B J.New Exact Solutions for the (2+1)-dimensional Generalized Broer-Kaup System[J].Applied Mathematics and Computation,2008,199:572-580.doi:10.1016/j.amc.2007.10.1012
[12] CLARKSON P A.Painleve Equations-nonlinear Special Functions[J].Computers and Appllied Mathematics,2003,153:127-140.
[13] LIU H Z,LI W R.The Exact Analytic Solutions of a Nonlinear Differential Iterative Equation[J].Nonlinear Analysis:Theory,Methods and Applications,2008,69:2466-2478.doi:10.1016/j.na.2007.08.025
[14] LIU H,QIU F.Analytic Solutions of an Iterative Equation with First Order Derivative[J].Annals Differential Equations,2005,21:337-342.
[15] LIU H Z,LI W R.Discussion on the Analytic Solutions of the Second-order Iterative Differential Equation[J].Bulletin-Korean Mathematical Society,2006,43:791-804.
[16] LBRAGIMOV N H.A New Conservation Theorem[J].Journal of Mathematical Analysis and Applications,2007,333:311-328.doi:10.1016/j.jmaa.2006.10.078
[17] BANSAL A,GUPTA R K.Modified (G'/G)-expansion Method for Finding Exact Wave Solutions of the Coupled Klein-Gordon-Schr dinger Equation[J].Applied Mathematics and Computation,2012,35:1175-1187.doi:10.1002/mma.2506
[18] FAN E G,ZHANG J.Applications of the Jacobi Elliptic Function Method to Special-type Nonlinear Equations[J].Physics Letter A,2002,305:383-392.doi:10.1016/s0375-9601(02)01516-5
[19] HE J H.Exp-function Method for Nonlinear Wave Equation[J].Chaos,Solitons and Fractals,2006,30:700-708.doi:10.1016/j.chaos.2006.03.020
[20] KHATER A H,HELAL M A,ElKALAAWY O H.Bäcklund Transformations:Exact Solutions for the KdV and the Calogero-Degasperis-Fokas MKdV Equations[J].Mathematical Methods in the Applied Sciences,1998,21:719-731.
[21] ZEDAN H A,TANTAWY S S.Exact Solutions for a Perturbed Nonlinear Schr dinger Equation by Using Bäcklund Transformations[J].Mathematical Methods in the Applied Sciences,2009,32:1068-1081.doi:10.1007/s11071-013-1030-5
[22] BAI C L,BAI C J,ZHAO H.Travelling Wave Solutions for the Generalized Zakharov-Kuznetsov Equation with Higher-order Nonlinear Terms[J].Applied Mathematics and Computation,2009,208:144-155.doi:10.1016/j.amc.2008.11.020
[23] ZHANG Y Y,WANG G W,LIU X Q.Symmetry Reductions and Exact Solutions of the (2+1)-dimensional Jaulent-Miodek Equation[J].Applied Mathematics and Computation,2012,219:911-916.doi:10.1016/j.amc.2012.06.069
[24] BRUZÓN M S,GANDARIAS M L.Symmetry Reductions and Traveling Wave Solutions for the Krichever-Novikov Equation[J].Mathematical Methods in the Applied Sciences,2012,35:869-876.doi:10.1002/mma.1578
[25] ElSHIEKH R M.New Exact Solutions for the Variable Coefficient Modified KdV Equation Using Direct Reduction Method[J].Mathematical Methods in the Applied Sciences,2013,36:1-4.doi:10.1002/mma.2561