基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解

杨小锋; 邓子辰; 魏乙

doi:10.3879/j.issn.1000-0887.2015.10.006

基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解

doi: 10.3879/j.issn.1000-0887.2015.10.006

¹西北工业大学应用数学系, 西安 710072;²西北工业大学工程力学系, 西安 710072

基金项目: 高校博士点基金(20126102110023);中央高校基本科研业务费专项资金(3102014JCQ01035)

详细信息

作者简介:
杨小锋(1978—), 男，陕西人，博士生(E-mail: yangxiaofeng@nwsuaf.edu.cn);邓子辰(1964—), 男，辽宁人，教授, 博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn);魏乙(1980—), 男，山东人，博士生(E-mail: weiyiwy@126.com).

中图分类号: O175.2
计量
- 文章访问数: 1669
- HTML全文浏览量: 158
- PDF下载量: 864
- 被引次数: 0
出版历程
- 收稿日期: 2015-06-24
- 修回日期: 2015-07-23
- 刊出日期: 2015-10-15

Traveling Wave Solutions to the Davey-Stewartson Equation With the Riccati-Bernoulli Sub-ODE Method

¹Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P.R.China;²Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

摘要

摘要: Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程, 再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组, 求解非线性代数方程组就能直接得到非线性偏微分方程的行波解.对Davey-Stewartson方程应用这种方法, 得到了该方程的精确行波解.同时也得到了该方程的一个Backlund变换.所得结果与首次积分法的结果作了比较.Riccati-Bernoulli辅助常微分方程方法是一种简单、有效地求解非线性偏微分方程精确解的方法.
- Riccati-Bernoulli辅助常微分方程方法 /
- Davey-Stewartson方程 /
- 行波解 /
- Backlund变换
Abstract: The Riccati-Bernoulli subsidiary ordinary differential equation (sub-ODE) method was proposed to construct the exact traveling wave solutions to the nonlinear partial differential equations (NLPDEs). Through traveling wave transformation, the NLPDE was reduced to a nonlinear ODE. With the aid of the Riccati-Bernoulli sub-ODE, the nonlinear ODE was converted into a set of nonlinear algebraic equations. The exact traveling wave solutions to the NLPDE were obtained as soon as this set of nonlinear algebraic equations were solved. Application of this method to the Davey-Stewartson equation directly gave the exact traveling wave solutions. The Bcklund transformation of the Davey-Stewartson equation was also given. The results were compared with those of the first-integral method. The proposed method is effective and easy to be generalized to deal with other types of nonlinear partial differential equations.
- Riccati-Bernoulli sub-ODE method /
- Davey-Stewartson equation /
- traveling wave solution /
- Backlund transformation

HTML全文

参考文献(25)

[1]	Ablowitz M J, Clarkson P A.Solitons, Nonlinear Evolution Equations and Inverse Scattering [M]. Cambridge: Cambridge University Press, 1991.
[2]	Ablowitz M J, Segur H.Solitons and Scattering Transformation [M]. Philadelphia: SIAM Press, 1981.
[3]	Rogers C, Schief W K.Backlund and Darboux Transformation Geometry and Modern Applications in Solitons Theory [M]. Cambridge: Cambridge University Press, 2002.
[4]	Gu C H, Hu H S. A unified explicit form of Bcklund transformations for generalized hierarchies of KdV equations[J].Letters in Mathematical Physics,1986,11(4): 325-335.
[5]	Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons[J].Phys Rev Lett,1971,27(18): 1192-1194.
[6]	Hirota R, Ito M. Exact solution of the modified Korteweg-de Vries equation for multiple collisions of solitons[J].Journal of the Physical Society of Japan,1972,33(5): 1456-1458.
[7]	Hirota R.The Direct Method in Soliton Theory [M]. Cambridge: Cambridge University Press, 2004.
[8]	WANG Ming-liang. Solitary wave solutions for variant Boussinesq equations[J].Physics Letters A,1995,199（3/4）: 169-172.
[9]	Wang M L, Zhou Y B. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics[J].Physics Letters A,1996,216(1): 67-75.
[10]	BAI Cheng-lin. Extended homogeneous balance method and Lax pairs, Bcklund transformation[J].Communications in Theoretical Physics,2002,37（6）: 645-648.
[11]	Taghizadeh N, Mirzazadeh M, Filiz T. The first-integral method applied to the Eckhaus equation[J].Applied Mathematics Letters,2012,25（5）: 798-802.
[12]	Lu B. The first integral method for some time fractional differential equations[J].Journal of Mathematical Analysis and Applications,2012,395（2）:684-693.
[13]	WANG Ming-liang, LI Xiang-zheng, ZHANG Jin-liang. The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics[J].Physics Letters A,2008,372（4）: 417-423.
[14]	ZHANG Hui-qun. New application of the (G′/G)-expansion method[J]. Communications in Nonlinear Science and Numerical Simulation,2009,14(8): 3220-3225.
[15]	Wazwaz A M. The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations[J].Applied Mathematics &Computation,2005,167（2）: 1196-1210.
[16]	YAN Zhen-ya. Abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional integrable Davey-Stewartson-type equation via a new method[J].Chaos, Solitons & Fractals,2003,18（2）: 299-309.
[17]	McConnell M, Fokas A S, Pelloni B. Localised coherent solutions of the DSI and DSII equations—a numerical study[J].Mathematics and Computers in Simulation,2005,69（5/6）: 424-438.
[18]	Davey A, Stewartson K. On three-dimensional packets of surfaces waves[J].Proceedings of the Royal Society of London, Series A,1974,338: 101-110.
[19]	Djordjevic V D, Redekopp L G. On two-dimensional packets of capillary-gravity wave[J].Journal of Fluid Mechanics,1977,79(4): 703-714.
[20]	Novikov S, Manakov S V, Pitaevskii L P, Zakharov V E.Theory of Solitons, the Inverse Scattering Method [M]. New York: Consultants Bureau Press, 1984.
[21]	Zakharov V E.The Inverse Scattering Method, in Soliton [M]. Heidelberg: Springer Press, 1980.
[22]	Zedan H A, Tantawy S S. Solutions of Davey-Stewartson equations by homotopy perturbation method[J].Computational Mathematics and Mathematical Physics,2009,49(8): 1382-1388.
[23]	Ghidaglia J M, Saut J C. On the initial value problem for the Davey-Stewartson systems[J].Nonlinearity,1990,3(2): 475-506.
[24]	Jafari H, Sooraki A, Talebi Y, Biswas A. The first integral method and traveling wave solutions to Davey-Stewartson equation[J].Nonlinear Analysis: Modelling and Control,2012,17(2): 182-193.
[25]	张金良, 任东锋, 王明亮, 方宗德. Davey-Stewartson Ⅰ的周期波解[J]. 数学物理学报, 2005,25(2): 213-219.(ZHANG Jin-liang, REN Dong-feng, WANG Min-liang, FANG Zhong-de. The periodic wave solutions for the Davey-Stewartson Ⅰ[J].Acta Mathematica Scientia,2005,25(2): 213-219.(in Chinese))

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1669
HTML全文浏览量: 158
PDF下载量: 864
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解

doi: 10.3879/j.issn.1000-0887.2015.10.006

作者简介:
杨小锋(1978—), 男，陕西人，博士生(E-mail: yangxiaofeng@nwsuaf.edu.cn);邓子辰(1964—), 男，辽宁人，教授, 博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn);魏乙(1980—), 男，山东人，博士生(E-mail: weiyiwy@126.com).

计量

Traveling Wave Solutions to the Davey-Stewartson Equation With the Riccati-Bernoulli Sub-ODE Method

计量

目录

留言板

基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解

doi: 10.3879/j.issn.1000-0887.2015.10.006

作者简介: 杨小锋(1978—), 男， 陕西人， 博士生(E-mail: yangxiaofeng@nwsuaf.edu.cn);邓子辰(1964—), 男， 辽宁人， 教授, 博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn);魏乙(1980—), 男， 山东人， 博士生(E-mail: weiyiwy@126.com).

计量

出版历程

Traveling Wave Solutions to the Davey-Stewartson Equation With the Riccati-Bernoulli Sub-ODE Method

计量

出版历程

目录

作者简介:
杨小锋(1978—), 男，陕西人，博士生(E-mail: yangxiaofeng@nwsuaf.edu.cn);邓子辰(1964—), 男，辽宁人，教授, 博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn);魏乙(1980—), 男，山东人，博士生(E-mail: weiyiwy@126.com).