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
扩展的(2+1)维Jaulent-Miodek方程的显式解和守恒律
- 聊城大学 数学科学学院, 山东 聊城 252059
-
DOI：10.13763/j.cnki.jhebnu.nse.2016.05.002
Explicit Solutions,Conservation Laws of the Extended (2+1)-dimensional Jaulent-Miodek Equation
摘要/Abstract
摘要：
通过直接对称方法，得到了扩展的（2+1）维Jaulent-Miodek方程的经典李对称，并且利用对称得到了该方程的相似约化方程和群不变解.通过解约化方程得到了大量新的精确解，其中包括Weierstrass周期解、椭圆周期解、三角函数解等.最后，利用得到的对称和共轭方程，求得了该方程的守恒律.
Abstract：
By applying the direct symmetry method, the classical Lie symmetry for the extended (2+1)-dimensional Jaulent-Miodek equation were obtained, and further the symmetry reductions and group invariant solutions were obtained from this symmetry.Many new exact solutions of this equation were obtained through the symmetry,which include Weierstrass periodic solutions,elliptic periodic solutions,and triangular function solutions.Finally,the conservation laws of the equation were obtained by using the symmetry and adjoint equations.
关键词
关键词：
Jaulent-Miodek方程
;
李点对称
;
相似约化
;
精确解
;
守恒律
Key words：
Jaulent-Miodek equation
;
Lie point symmetry
;
similarity reduction
;
exact solution
;
conservation laws
参考文献 16
- [1] KUMEI G,BLUMAN G W.Symmetries and Differential Equations[M].New York:Springer-verlag,1989.doi:10.1007/978-1-4757-4307-4
- [2] LIU H Z,LI J B.Symmetry Reductions,Dynamical Behavior and Exact Explicit Solutions to the Gordon Types of Equations[J].Appl Math Comput,2014,257:144.doi:10.1016/j.cam.2013.08.022
- [3] HE J H,WU X H.Exp-function Method for Nonlinear Wave Equation[J].Chaos,Solitions and Fractals,2006,3(11):700.doi:10.1016/j.chaos.2006.03.020
- [4] WAZWAZ A M.The Extended Tanh Method for the Zakharov-Kuznetsov (ZK) Equation,the Modified ZKequation,and Its Generalized Forms[J].Commun Nonlinear Sci Numer Simul,2008,13(6):1039.doi:10.1016/j.cnsns.2006.10.007
- [5] ZHAO X Q,ZHI H Y,ZHANG H Q.Improved Jacobi-function Method with Symbolic Computation to Construct New Double-periodic Solutions for the Generalized Ito System[J].Chaos,Solitions and Fractals,2006,28(1):112.doi:10.1016/j.chaos.2005.05.016
- [6] ZHANG H Q.Extended Jacobi Elliptic Function Expansion Method and its Applications[J].Commun Nonlinear Sci Numer Simul,2007,12(5):627.doi:10.1016/j.cnsns.2005.08.003
- [7] ZHANG J F,DAI C Q,YANG Q,et al.Variable-coefficient F-expansion Method and Its Application to Nonlinear Schr dinger Equation[J].Opt Commun,2005,252(4):408.doi:10.1016/j.optcom.2005.04.043
- [8] 陈美,刘希强,王猛.对称正则长波方程组的对称、精确解和守恒律[J].量子电子学报,2011,29(5):21.doi:10.3969/j.issn.1007-5461.2011.05.004
- [9] CONTE R,MUSETTE M.Painleve Analysis and Backlund Transformation in the Kuramoto Sivashinsky Equation[J].J Phys A:Math Gen,1989,22(2):169.http://dx.doi.org/10.1088/0305-4470/22/2/006
- [10] FAN E G.Uniformly Constructing a Series of Explicit Exact Solutions to Nonlinear Equations Mathematical Physics[J].Chaos,Solitions and Fractals,2003,16(5):819.doi:10.1016/S0960-0779(02)00472-1
- [11] FENG D H,LI J B.Bifurcations of Travelling Wave Solutions for Jaulent-Miodek Equations[J].Appl Math Mech-Engl Ed,2007,28:999.doi:10.1007/s10483-007-0802-1
- [12] 杜兴华.用试探方程法求Jaulent-Miodek方程的新的精确行波解[J].数学的实践与认知,2010,40(6):204.
- [13] KAVITHA L,SATHISHKUMAR P,NATHIYAA T,et al.Cusp-like Singular Soliton Solutions of Jaulent-Miodek Equation Using Symbolic Computation[J].Physica Scripta,2009,79(3):035403.http://dx.doi.org/10.1088/0031-8949/79/03/035403
- [14] ZHANG Y Y,LIU X Q.Symmetry Reductions and Exact Solutions of the (2+1)-dimensional Jaulent-Miodek Equation[J].Appl Math Comput,2012,219(10):911.doi:10.1016/j.amc.2012.06.069
- [15] XIN X P,LIU X Q,ZHANG L L.Explicit Solutions of the Bogoyavlensky-Konoplechenko Equation[J].Appl Math Comput,2010,215(10):3669.doi:10.1016/j.amc.2009.11.005
- [16] 张颖元,王岗伟,刘希强.(2+1)维非线性发展方程的对称约化和显式解[J].量子电子学报,2012,29(4):411. doi:10.3969/j.issn.1007-5461.2012.04.005