AAM  >> Vol. 5 No. 3 (August 2016)

    修正的简单方程法与sine-Godon方程和广义的变系数KdV-mKdV方程的精确解
    The Modified Simple Equation Method and the Exact Solutions for the sine-Gordon Equation and the Generalized Variable-Coefficient KdV-mKdV Equation

  • 全文下载: PDF(518KB) HTML   XML   PP.443-449   DOI: 10.12677/AAM.2016.53055  
  • 下载量: 155  浏览量: 558   国家自然科学基金支持

作者:  

肖玲风,斯仁道尔吉:内蒙古师范大学数学科学学院,内蒙古 呼和浩特

关键词:
修正的简单方程法sine-Gordon方程变系数KdV-mKdV方程精确解The Modified Simple Equation Method sine-Gordon Equation Variable-Coefficient KdV-mKdV Equation Exact Solutions

摘要:
本文用修正的简单方程法对sine-Gordon方程和广义的变系数KdV-mKdV方程进行求解,并给出了它们的行波解,当给参数取特殊值时,便可以得到相应的精确行波解。

The modified simple equation method is used to construct the exact solutions for the sine-Gordon equation and the generalized variable-coefficient KdV-mKdV equation. Some exact solutions of the hyperbolic function form for the sine-Gordon equation and the generalized variable-coefficient KdV-mKdV equation are derived by the method. When taking special values of the parameters, the exact traveling wave solutions of the equations are derived from the exact solutions.

文章引用:
肖玲风, 斯仁道尔吉. 修正的简单方程法与sine-Godon方程和广义的变系数KdV-mKdV方程的精确解[J]. 应用数学进展, 2016, 5(3): 443-449. http://dx.doi.org/10.12677/AAM.2016.53055

参考文献

[1] Alowitz, M.J., Ramani, A. and Segur, H. (1978) Nonlinear Evolution Equations and Ordinary Differential Equations of Painlevé Type. Lettere al Nuovo Cimento, 23, 333-338.
http://dx.doi.org/10.1007/BF02824479
[2] Weiss, J., Tabor, M. and Carnevale, G. (1983) The Painlevé Property for Partial Differential Equations. Journal of Mathematical Physics, 24, 522.
http://dx.doi.org/10.1063/1.525721
[3] Wang, Y.-H. and Chen, Y. (2012) Bäcklund Transformations and Solutions of a Gene-ralized Kadomtsev-Petviashvili Equation. Communications in Theoretical Physics, 57, 217-322.
http://dx.doi.org/10.1088/0253-6102/57/2/10
[4] Sirendaoerji, T. (2006) New Exact Solitary Wave for Nonlinear Wave Equation with Fifth-Order Strong Nonlinear Term Constructed by Hyperbolic Function Type of Auxiliary Equation. Acta Physica Sinica, 55, 13-18.
[5] Wang, M.L., Li, X.Z. and Zhang, J.L. (2008) The G'/G-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations in Mathematical Physics. Physics Letters A, 372, 417-423.
http://dx.doi.org/10.1016/j.physleta.2007.07.051
[6] Khan, K. and Akbar, M.A. (2013) Exact and Solitary Wave Solutions for the Tzitzeica-Dodd-Bullough and the Modified KdV-Zakharov-Kuznetsov Equations Using the Modified Simple Equation Method. Ain Shams Engineering Journal, 4, 903-909.
http://dx.doi.org/10.1016/j.asej.2013.01.010
[7] 张哲, 李德生. 修正的BBM方程新的精确解[J]. 原子与分子物理学报, 2013, 30(5).
[8] Rubinstein, J. (1970) sine-Gordon Equation. Journal of Mathematical Physics, 11, 258-266.
http://dx.doi.org/10.1063/1.1665057
[9] Bratsos, A.G. (2007) The Solution of the Two-Dimensional sine-Gordon Equation Using the Method of Lines. Journal of Computational and Applied Mathematics, 206, 251-277.
[10] Meng, G.-Q., Gao, Y.-T., Yu, X., Shen, Y.-J. and Qin, Y. (2012) Painlevé Analysis, Lax Pair, Bäcklund Transformation and Multi-Soliton Solutions for a Generalized Variable-Coefficient KdV-mKdV Equation in Fluids and Plasmas. Physica Scripta, 85, 055010.
http://dx.doi.org/10.1088/0031-8949/85/05/055010