| 一类非线性偏微分方程的摄动解法 |
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| 引用本文： | 谢元喜.一类非线性偏微分方程的摄动解法[J].娄底师专学报,2005(5):15-17,44. |
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| 作者姓名： | 谢元喜 |
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| 作者单位： | 湖南人文科技学院物理系,湖南娄底417000 |
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| 摘 要： | 首先用行波变换将非线性偏微分方程转化为非线性常微分方程,然后采用摄动方法直接求解该非线性常微分方程,最后求得了非线性Klein-Gordon方程的二级近似解.这种方法也可进一步推广用于求其它非线性偏微分方程的近似解析解.
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| 关 键 词： | 非线性Klein-Gordon方程 行波变换 摄动解法 二级近似解 |
| 文章编号： | 1673-0712（2005）05-0015-03 |
| 收稿时间： | 2004-06-27 |
Perturbation Method for a Class of Nonlinear Partial Differential Equation |
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| XIE Yuan-xi.Perturbation Method for a Class of Nonlinear Partial Differential Equation[J].Journal of Loudi Teachers College,2005(5):15-17,44. |
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| Authors: | XIE Yuan-xi |
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| Abstract: | In this paper, nonlinear partial differential equation is transformed to nonlinear ordinary differential equation by virtue of traveling wave transformation method, and then straightforwardly solve it by taking advantage of perturbation method. Fi- nally, the second order approximate solutions of nonlinear Klein-Cordon equation are successfully obtained. It is not difficult to see that this method used herein is particularly simple and concise. We firmly believe that this approach used in our paper may be generalized to construct the approximately analytical sohtions to other nonlinear partial differential equations. |
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| Keywords: | nonlinear Klein-Cordon equation traveling wave transformation perturbation method second order approximate solution |
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