| 求一类偏微分方程解析新解的试探函数法 |
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| 引用本文： | 余德民,谢元喜,丁卫平.求一类偏微分方程解析新解的试探函数法[J].湖南第一师范学报,2011,11(4):122-124. |
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| 作者姓名： | 余德民 谢元喜 丁卫平 |
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| 作者单位： | 湖南理工学院,湖南岳阳,414006 |
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| 基金项目： | 湖南省自然科学基金，湖南省教育厅科研项目 |
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| 摘 要： | 利用速探函数法，应用到KdV方程和Burgers方程和KdV—Burgers方程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，可简洁求得一类非线性偏微分方程的精确新解，此方法可望进一步推广用于求解其他非线性偏微分方程。
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| 关 键 词： | KdV方程 Burgers方程 试探函数 解析解 |
A Trial Function Method for Seeking the Analytical New Solution to Partial Differential Equations |
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| YU De-ming,XIE Yuan-xi,DING Wei-ping.A Trial Function Method for Seeking the Analytical New Solution to Partial Differential Equations[J].Journal of First Teachers College of Hunan,2011,11(4):122-124. |
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| Authors: | YU De-ming XIE Yuan-xi DING Wei-ping |
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| Institution: | Department of Mathematics, Hunan Institute of Science and Technology, Yue yang 414006 |
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| Abstract: | It is not easy to solve the KdV equations, the Burgers equations and KdV-Burgers equations by the usual ways. While by making use of the trial function method, the KdV equations, the Burgers equations and KdV-Burgers equations can be reduced to a set of algebraic equations which can he easily solved, and their related co- efficients can be easily determined by the undetermined coefficients method. Then, the new analytical solutions to the KdV equations, the Burgers equations and KdV-Burgers equations can be successfully derived. This method may be generalized to construct the solutions of other nonlinear partial differential equations （PDES for short）. |
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| Keywords: | KdV equations Burgers equations trial function analytical solution |
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