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
Dodd-Bullough-Mikhailov方程的对称、约化和精确解
-
1. 聊城大学 东昌学院, 山东 聊城 252059;
2. 聊城大学 学报编辑部, 山东 聊城 252059 -
DOI：10.13763/j.cnki.jhebnu.nse.2015.06.002
Symmetry Reductions and Exact Solutions of Dodd-Bullough-Mikhailov Equation
摘要/Abstract
摘要：
利用经典李群方法得到了Dodd-Bullough-Mikhailov(DBM)方程的对称、约化,通过解约化方程得到了该方程的一些行波解,并研究了DBM方程的守恒律.
Abstract：
Using the classical Lie group method,We find the classical symmetry and reductions of the Dodd-Bullough-Mikhailov (DBM) equation.Many kinds of exact traveling wave solutions of the DBM equation are derived by solving the reduced equations.We also give the conservation laws of the DBM equation.
关键词
参考文献 16
- [1] WAZWAZ A M.The Tanh Method for Travelling Wave Solution of Nonlinear Wave Equations[J].Appl Math Comput,2007,187:1131-1142.
- [2] FAN E G,ZHANG J.Applications of the Jacobi Elliptic Function Method to Special-type Nonlinear Equations[J].Phys Lett A,2002,305:383-392.
- [3] FU Z T,LIU S K,LIU S D,et al.New Jacobi Elliptic Function Expansion and New Periodic Solutions of Nonlinear Wave Equations[J].Phys Lett A,2001,290:72-76.
- [4] WANG M L.Exact Solutions of a Compound KdV-burgers Equation[J].Phys Lett A,1996,213:279-287.
- [5] WADATI M.Wave Propagation in Nonlinear Lattice I[J].Phys Soc Jpn,1975,38:673-680.
- [6] BASSOM A P,CLARKSON P A,HICKS A C.Backlund-transformations and Solution Hierarchies for the 4th Painleve Equation[J].Studies in Applied Mathematics,1995,95(1):1-71.
- [7] ABLOWITZ M J,SEGUR H.Solitons and Inverse Scattering Transform[M].Philadelphia:SIAM,1981.
- [8] LIU J,YANG K.The Extended F-expansion Method and Exact Solutions of Nonlinear PDEs[J].Chaos Soliton Fract,2004,22:111-121.
- [9] HIROTA R.Exact Solution of the KdV Equation for Multiple Collisions of Solitons[J].Phys Rev Lett,1971,27:1192-1194.
- [10] HE J H,WU X H.Exp-function Method for Nonlinear Wave Equation[J].Chaos Soliton Fract,2006,3:700-708.
- [11] 刘庆松,周相泉.(2+1)维Zoomeron方程的新精确解[J].河北师范大学学报:自然科学版,2014,38(3):229-232.
- [12] WAZEAZ A M.The Tanh Method:Solitons and Periodic Solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough Equations[J].Chaos Solitons Fract,2005,25:55-63.
- [13] WANG M,LI X,ZHANG J.The (G'/G)-expansion Method and Traveling Wave Solutions of Nonlinear Evolution Equations in Mathematical Physics[J].Phys Lett A,2008,372(4):417-423.
- [14] NAIL H I.A New Conservation Theorem[J].Math Anal Appl,2007,333:311-328.
- [15] XIN X P,LIU XQ,ZHANG L L.Symmetry Reduction,Exact Solutions and Conservation Laws of the Sawada-Kotera-Kadomtsev-Petviashvili Equation[J].Appl Math Comput,2010,216:1065-1071.
- [16] WANG G W,LIU X Q,ZHANG Y Y.Symmetry Reduction,Exact Solutions and Conservation Laws of a New Fifth-order Nonlinear Integrable Equation[J].Commun Nonlinear Sci Numer Simulat,2013,18:2313-2320.