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数学与物理
应用数学进展
Vol. 5 No. 3 (August 2016)
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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
DOI:
10.12677/AAM.2016.53055
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被引量
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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。
Abstract:
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
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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.
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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
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