Notes on Solutions to Burgers-type Equations 被引量：3

Notes on Solutions to Burgers-type Equations

下载PDF

导出

摘要 A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wave solution are obtained,and it is shown that this is a powerful method to solve nonlinear equations with odd-order and even-order derivatives simultaneously.

作者 FUZun-Tao LIUShi-Da LIUShi-Kuo

机构地区 SchoolofPhysics StateKeyLaboratoryforTurbulenceandComplexSystem

出处《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第4期527-530,共4页 理论物理通讯（英文版）

基金国家自然科学基金

关键词 Burgers-type equations travelling wave solution solitary wave solution 伯格斯型方程行波解孤波解数学物理方法

分类号 O411.1 [理学—理论物理]

引文网络
相关文献

参考文献18

1[1]P.K.Shukla,N.N.Rao,M.Y.Yu,et al.,Phys.Rep.138(1986)1.
2[2]M.J.Ablowitz and H.Segur,Solitons and the Inverse Scattering Tranforms,Philadelphia,SIAM(1981).
3[3]J.M.Burgers,Adv.Appl.Mech.1(1946)171.
4[4]S.D.Liu and S.K.Liu,Commun.Theor.Phys.(Beijing,China)16(1991)497.
5[5]S.D.Liu and S.K.Liu,Science in China A35(1992)576.
6[6]D.J.Benney,J.Math.Phys.45(1966)52.
7[7]T.Kawahara,Phys.Rev.Lett.51(1983)381.
8[8]S.D.Liu,S.K.Liu,Z.H.Huang,and Q.Zhao,Prog.Natur.Sci.9(1999)912.
9[9]C.L.Bai,Phys.Lett.A288(2001)191.
10[10]Z.T.Fu,S.K.Liu,and S.D.Liu,Phys.Lett.A299(2002)507.

同被引文献9

1谢元喜,唐驾时.求一类非线性偏微分方程解析解的一种简洁方法[J].物理学报,2004,53(9):2828-2830. 被引量：53
2谢元喜,唐驾时.对“求一类非线性偏微分方程解析解的一种简洁方法”一文的一点注记[J].物理学报,2005,54(3):1036-1038. 被引量：18
3谢元喜,唐驾时.A unified approach in seeking the solitary wave solutions to sine-Gordon type equations[J].Chinese Physics B,2005,14(7):1303-1306. 被引量：19
4谢元喜,苏卡林,朱曙华.A simple approach to solving double sinh–Gordon equation[J].Chinese Physics B,2008,17(5):1581-1586. 被引量：3
5范恩贵,张鸿庆.非线性孤子方程的齐次平衡法[J].物理学报,1998,47(3):353-362. 被引量：265
6张玉峰,张鸿庆.Burgers-KdV方程的二类行波解[J].应用数学和力学,2000,21(10):1009-1012. 被引量：8
7刘式适,傅遵涛,刘式达,赵强.Jacobi椭圆函数展开法及其在求解非线性波动方程中的应用[J].物理学报,2001,50(11):2068-2073. 被引量：351
8吕克璞,石玉仁,段文山,赵金保.KdV-Burgers方程的孤波解[J].物理学报,2001,50(11):2074-2076. 被引量：78
9FUZun-Tao,ZHANGLin,LIUShi-Da,LIUShi-Kuo.Basic Pattern in Atmospheric Turbulence Model[J].Communications in Theoretical Physics,2004,41(6):845-848. 被引量：3

引证文献3

1Xie Yuanxi(Dept. of Physics and Electric Information,Hunan Institute of Science and Technology,Yueyang 414000,Hunan).SOLUTIONS TO A CLASS OF NONLINEAR WAVE EQUATIONS[J].Annals of Differential Equations,2008,24(2):208-214.
2谢元喜,朱曙华.KdV-Burgers方程和KdV-Burgers-Kuramoto方程的精确解[J].安徽大学学报（自然科学版）,2007,31(6):44-47. 被引量：3
3谢元喜.Burgers方程的新解(英文)[J].吉首大学学报（自然科学版）,2008,29(5):5-9. 被引量：6

二级引证文献9

1王燕,孙福伟.变系数KdV-Burgers方程的精确解及其Bcklund变换[J].北方工业大学学报,2009,21(3):45-50. 被引量：4
2向阳洁.科技期刊中3个与范围有关的问题[J].吉首大学学报（社会科学版）,2010,31(3):139-141. 被引量：1
3邱美兰,李德旺,林远华.非线性反应-扩散方程的精确解[J].西南师范大学学报（自然科学版）,2011,36(2):17-19. 被引量：1
4刘清鉴.大胆开拓深入探索——读《中亚五国对外关系》一书[J].东欧中亚研究,2000(1):91-92.
5林府标.Burgers方程的一类自相似解[J].数学的实践与认识,2016,46(9):241-246. 被引量：5
6何姝琦,陈立.利用(g′/g^2)展开法求解KdV-Burgers方程和KdV-Burgers-Kuramoto方程[J].纺织高校基础科学学报,2016,29(3):327-332. 被引量：2
7林府标,张千宏.双sine-Gordon方程的新精确解及其应用[J].西南大学学报（自然科学版）,2021,43(3):74-81. 被引量：3
8赵临龙.利用Riccati方程求解Burgers方程再探[J].数学的实践与认识,2023,53(12):243-250.
9张庆慧.常系数KdV-Burgers方程的李对称分析和精确解[J].黑龙江科技信息,2015(10):88-89.

1M.H.M.Moussa,R.A.K.Omar,Rehab M.El-Shiekh,H.R.El-Melegy.Nonequivalent Similarity Reductions and Exact Solutions for Coupled Burgers-Type Equations[J].Communications in Theoretical Physics,2012,57(1):1-4. 被引量：2
2FUZun-Tao,ZHANGLin,LIUShi-Da,LIUShi-Kuo.Basic Pattern in Atmospheric Turbulence Model[J].Communications in Theoretical Physics,2004,41(6):845-848. 被引量：3
3张玉峰,张鸿庆.TWO TYPES OF TRAVELING WAVE SOLUTIONS TO BURGERS-KdV EQUATIONS[J].Applied Mathematics and Mechanics(English Edition),2000,21(10):1119-1122.
4Hongwei Yang 1 , Yunhu Wang 2 , Wencai Zhao 1 (1. Information School, Shandong University of Science and Technology, Qingdao 266510,2. Software Enginearing Institute, East China Normal University, Shanghai 200062).PAINLEV PROPERTY OF BURGERS-KDV EQUATION AND ITS EXACT SOLUTIONS[J].Annals of Differential Equations,2010,26(4):465-470.
5Jiefang ZhangInstitute of Nonlinear Physics and Deraftment of Physics, Zhejiang Normal University, Jinhua 321004, Zhejiang, P. R. China.New Solitary Wave Solution of the Combined KdV and mKdV Equation[J].浙江海洋学院学报（人文科学版）,1997,14(3):30-34.
6闻小永,高以天,薛玉山,郭睿,齐凤华,于鑫.Integrable Hierarchy Covering the Lattice Burgers Equation in Fluid Mechanics:N-fold Darboux Transformation and Conservation Laws[J].Communications in Theoretical Physics,2012,58(9):323-330. 被引量：1
7LINDong.Solitary wave solution for Beji-type Boussinesq equation[J].海南师范学院学报（自然科学版）,2004,17(4):329-332.
8ZHANGJin-liang,ZHANGLing-yuan,WANGMing-liang.Periodic Wave Solutions for Konopelchenko-Dubrovsky Equation[J].Chinese Quarterly Journal of Mathematics,2005,20(1):72-78. 被引量：1
9吕咸青.Stability of the Korteweg-de Vries Solitary Wave Solution[J].Applied Mathematics and Mechanics(English Edition),1994,15(9):885-886.
10FUZun-Tao,DENGLian-Tang,LIUShi-Kuo,LIUShi-Da.Solutions to Generalized mKdV Equation[J].Communications in Theoretical Physics,2003,40(6X):641-644. 被引量：4

Communications in Theoretical Physics

2004年第4期

浏览历史

内容加载中请稍等...

Notes on Solutions to Burgers-type Equations 被引量：3

参考文献18

同被引文献9

引证文献3

二级引证文献9

相关作者

相关机构

相关主题

浏览历史