| 广义变系数KDV方程的对称及其群不变解 |
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| 引用本文： | 凌旭东,;蔡国梁,;潘小霞. 广义变系数KDV方程的对称及其群不变解[J]. 佳木斯工学院学报, 2008, 0(1): 89-91 |
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| 作者姓名： | 凌旭东, 蔡国梁, 潘小霞 |
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| 作者单位： | [1]镇江船艇学院数学教研室,江苏镇江212009; [2]江苏大学理学院,江苏镇江212009 |
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| 基金项目： | 基金项目：国家自然科学基金项目（70571030）;江苏省教育厅基金项目（03SJB790008）. |
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| 摘 要： | 利用经典李对称的方法对广义变系数KDV方程进行研究，利用这种方法得到了该方程的一个新的精确解，这种方法的基本思路是通过对称约化将原来较难求解的偏微分方程转化为较易求解的常微分方程进行求解，实例证明这种方法具有一般性，适合于求一大类变系数的非线性演化方程。
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| 关 键 词： | 对称约化 变系数 KdV方程 群不变解 |
Symmetry Reduction and Group-invariant Solutions of the General Variable Coefficient KDV Equation |
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| Affiliation: | LING Xu-dong, CAI Guo-liang, WU Hui-Qin(1.Zhenjiang Water Craft College, Zhenjiang 212013, China; 2. Faculty of Science, Jiangsu University, Zhenjiang 212013, China) |
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| Abstract: | In this article, the solutions about the general variable coefficient Kdv equation were studied by using the classical lie symmetry method. Symmetries were used to obtain reduced equations and exact solutions. In this method, the PDE which is difficult to solve is convert to ODE which is easier to solve based on symmetry reduction. The fulfillment proved that this method is general, and suitable for solving a major type nonlinear evolving equations. |
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| Keywords: | symmetry reduction variable coefficient KDV equation group - invariant solution |
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