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
Lie Symmetries and Exact Solutions of a New Modified VN System
摘要/Abstract
摘要：
利用改进的CK直接方法,研究了修正VN方程组,建立了该方程组新、旧解之间的关系,基于此关系推广了方程组的解.同时,得到了该方程组的对称和约化,通过求解约化方程,得到修正的VN方程组许多新的精确解,包括幂级数解、艾米尔函数解、雅克比椭圆函数解等.
Abstract：
In this paper,we study the modified VN system by using an improved direct CK method,a relationship is constructed between the new solutions and the old ones of the modified VN system.Based on the relationship,new solutions are obtained by using a given solution of the equation.At the same time,the symmetry of the modified VN system is also obtained.By solving the reduction equation,some kinds of explicit solutions of the modified VN system are obtained,including the power series solution,the Airy function solution and Jacobi elliptic function solution.
关键词
Key words：
modified CK's direct method
;
modified VN system
;
symmetry reduction
;
exact solutions
参考文献 19
- [1] LIU X Q,YAN Z L.Some Exact Solutions of the Variable Coefficient Schrödinger Equation[J].Commun Nonlinear Sci Numer Simulat,2007,12(8):1355-1359.doi:10.1016/j.cnsns.2006.01.009
- [2] ROGERS C,SCHIEF W K.Bäcklund and Darboux Transformations,Geometry and Morden Applications in Soliton Theory[M].Cambridge:Cambridge University Press,2002.doi:10.1017/CB09780511606359
- [3] 冯春明,刘庆松.Dodd-Bullough-M:khailov方程的对称、约化和精确解[J].河北师范大学学报(自然科学版),2015,39(6):468-472.doi:10.13763/j.cnki.jhebnu.nse.2015.06.002
- [4] ABDOU M A.The Extended F-expansion Method and Its Application for a Class of Nonlinear Evolution Equation[J].Chaos Soliton Fract,2007,31(1):95-104.doi:10.1016/j.chaos.2005.09.030
- [5] HE J H,WU X H.Exp-function Method for Nonlinear Wave Equation[J].Chaos Soliton Fract,2006(3):700-708.doi:10.1016/j.chaos.2006.03.020
- [6] LIU X Q.Similarity Reductions and Similarity Solutions of the(3+1)-dimensional Kadomtsev-Petviashvili Equation[J].Chin Phys Lett,2008,25:3527-3530.
- [7] LIU Xiqiang,JIANG Song.The Sech-Tanh Method and Its Applications[J].Phys Lett A,2002,8(4):253-258.doi:10.1063/r.1320859
- [8] 陈美,刘希强.Konopelchenko-Dubrovsky方程组的对称、精确解和守恒律[J].纯粹数学与应用数学,2011,27(4):533-539
- [9] XIN X P,LIU X Q,ZHANG L L.Symmetry Reduction,Exact Solutions and Conservation Laws of the Modified Kadomtzev-Patvishvili-Ⅱ Equation[J].Phys Lett,2011,28(2):020201-1-020201-4.doi:10.1088/0256-307x/28121020201
- [10] ZHANG L H,LIU X Q.New Exact Solutions and Conservation Laws to (3+1)-dimensionalPotential-YTSF Equation[J].Communications in Theoretical Physics,2006,45(3):487-492.
- [11] CLARKSON P A,KRUSKAL M D.New Similarity Solutions of the Boussinesq Equation[J].Journal of Mathematical Physics,1989,30:2201-2213.doi:10.1063/1.528613
- [12] WANG J M.Construction of New Exact Traveling Wave Solutions to (2+1)-dimensional mVN Equation[J].International Journal of Nonlinear Science,2010,9:325-329.
- [13] ZHAO X,ZHI H,ZHANG H.Improved Jacobi-function Method with Symbolic Computation to Construct New Double-periodic Solutions for the Generalized Ito System[J].Chaos Solitons & Fractals,2006,28(1):112-126.doi:10.1016/j.chaos.2006.01.090
- [14] BAI C L,ZHAO H.A Method for Solving Initial-value Problem and Finding Exact Solutions of Nonlinear Partial Differential Equations[J].Czechoslovak Journal of Physics,2005,55(6):643-650.doi:10.1007/s10582-005-0068-0
- [15] EMMANUEL Y.On Exact Solutions of the Coupled Klein-Gordon-Schrödinger and the Complex Coupled KdV Equations Using Mapping Method[J].Chaos Solitons and Fractals,2004,2:209-229.doi:10.1016/j.chaos.2003.10.028
- [16] YAN Z Y,ZHANG H Q.New Explicit Solitary Wave Solutions and Periodic Wave Solutions for Whitham-Broer-Kaup Equation in Shallow Water[J].Phys Lett A,2001,285:355-362.doi:10.1007/s11401-012-0697-0
- [17] WANG M L,LI X Z.The Expansion Method and Traveling Wave Solution of Nonlinear Evolution Equation in the Mathematical Physics[J].Phy Lett A,2008,372:417-423.doi:10.1007/s11408-030-0752-0
- [18] PETER A C.Painleve Equations-Nonlinear Spccial Functions[J].Computer Appl Math,2003,153:127-140.doi:10.1016/s037-0427(02)00589-7
- [19] YAN Z L,LIU X Q.Symmetry and Similarity Solutions of Variable Coefficients Generalized Zakharov-Kuznetsov Equation[J].Appl Math Comput,2006,180:288-294.doi:10.1016/j.amc.2005.12.021