| 变系数mKdV方程的椭圆函数周期解 |
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| 引用本文： | 陈自高,连汝续.变系数mKdV方程的椭圆函数周期解[J].科技导报(北京),2011,29(10). |
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| 作者姓名： | 陈自高 连汝续 |
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| 作者单位： | 华北水利水电学院数学与信息科学学院,郑州,450011 |
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| 基金项目： | 河南省教育厅自然科学基金项目，河南省科技厅自然科学基金项目 |
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| 摘 要： | 通过引入一个波变换,将变系数mKdV方程约化为常微分方程.假设方程的系数满足特定的约束条件,借助符号计算软件Mathematica和扩展的F-展开函数法,在拟设法、齐次平衡原理和Jacobi椭圆函数展开法的基础上,求得了精确解的浓缩公式.利用第一类椭圆方程中P,Q,R的不同取值与相应的F(ξ)值之间的关系,从解的浓缩公式中,得到了丰富的显式精确解,特别是以两个不同的Jacobi椭圆函数表示的精确解.在极限的情况下,即当模疗m→1或m→0时,这些解退化为相应的类孤立波解和三角函数表示的精确解.该方法具有直接、简洁的特点,可以用来求解更多的在数学物理、自然科学和应用科学等领域出现的非线性偏微分方程的精确解.
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| 关 键 词： | 精确解 类孤立波解 扩展的F-展开法 变系数mKdV方程 |
Solutions of mKdV Equation with Variable Coefficients in Jacobi Elliptic and Periodic Functions |
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| CHEN Zigao,LIAN Ruxu.Solutions of mKdV Equation with Variable Coefficients in Jacobi Elliptic and Periodic Functions[J].Science & Technology Review,2011,29(10). |
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| Authors: | CHEN Zigao LIAN Ruxu |
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| Institution: | CHEN Zigao,LIAN Ruxu Department of Mathematics and Information Science,North China University of Water Resources and Electric Power,Zhengzhou 450011,China |
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| Abstract: | The mKdV equation with variable coefficients is reduced to an ordinary differential equation through a traveling wave transformation.With the aid of the symbolic computation software Mathematica as well as the extended F-expansion method recently proposed on the basis of the analogical method,the homogeneous balance principle and Jacobian elliptic function method,the concentrated formulas of exact solutions are derived if the coefficients of the mKdV equation satisfy some specific constraint conditions.By u... |
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| Keywords: | exact solution soliton-like solution extended F-expansion method mKdV equation with variable coefficients |
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