| KdV方程与Burgers方程的精确解 |
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| 引用本文： | 彭定忠,崔洁娟,叶芬花.KdV方程与Burgers方程的精确解[J].湖南理工学院学报,2012(2):17-19. |
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| 作者姓名： | 彭定忠 崔洁娟 叶芬花 |
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| 作者单位： | 湖南理工学院数学学院;长炼学校 |
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| 摘 要： | 利用试探函数法,将非线性偏微分方程转化为一个易于求解的代数方程,然后用待定系数法确定相应的常数,简洁地求得了一类非线性偏微分方程的精确解,并将此方法应用到KdV方程和Burgers方程.
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| 关 键 词： | 非线性偏微分方程 试探函数 待定系数法 精确解 |
The Exact Solution of the KdV Equation and The Burgers Equation |
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| PENG Ding-zhong,CUI Jie-juan,YE Fen-hua.The Exact Solution of the KdV Equation and The Burgers Equation[J].Journal of Hunan Institute of Science and Technology,2012(2):17-19. |
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| Authors: | PENG Ding-zhong CUI Jie-juan YE Fen-hua |
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| Institution: | 1.College of Mathematics,Hunan Institute of Science and Technology,Yueyang 414006;2.Hunan Changlian School,Yueyang 414012,China) |
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| Abstract: | By utilizing the trial function method,a class of nonlinear partial differential equations(PDEs for short) can be reduced to a set of algebraic equations which can be easily solved,then their related coefficients can be easily determined by the undetermined coefficients method,and the exact solution to this class of nonlinear PDEs can be successfully derived.Moreover,the method is applied to the KdV equation and the Burgers equation. |
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| Keywords: | nonlinear partial differential equation trial function method of undetermined coefficient exact solution |
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