| 广义变系数KdV-Burgers方程的微分不变量及群分类 |
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| 引用本文： | 郭美玉,刘希强,高洁. 广义变系数KdV-Burgers方程的微分不变量及群分类[J]. 量子电子学报, 2009, 26(2): 138-147. DOI: 10.3969/j.issn.1007-5461.2009.02.003 |
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| 作者姓名： | 郭美玉 刘希强 高洁 |
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| 作者单位： | 聊城大学数学科学学院,山东,聊城,252059;聊城大学数学科学学院,山东,聊城,252059;聊城大学数学科学学院,山东,聊城,252059 |
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| 摘 要： | 应用李无穷小不变规则,得到了广义变系数KdV-Burgers方程的连续等价变换.从等价代数开始,构造了一阶微分不变量并依据微分不变量对方程作了群分类.最后,通过等价变换将一般的变系数KdV-Burgers方程映射为常系数Burgers方程、KdV方程、KdV-Burgers方程.同时,也得到了变系数KdV-Burgers方程的一些精确解.
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| 关 键 词： | 非线性方程 李无穷小不变规则 微分不变量 群分类 广义变系数KdV-Burgers方程 |
| 收稿时间： | 2008-04-22 |
Differential invariants and group classification of KdV-Burgers equation |
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| GUO Mei-yu,LIU Xi-qiang,GAO Jie. Differential invariants and group classification of KdV-Burgers equation[J]. Chinese Journal of Quantum Electronics, 2009, 26(2): 138-147. DOI: 10.3969/j.issn.1007-5461.2009.02.003 |
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| Authors: | GUO Mei-yu LIU Xi-qiang GAO Jie |
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| Abstract: | By using Lie’s invariance infinitesimal criterion, the continuous equivalence transformations of a class of nonlinear KdV-Burgers equations with variable coefficients are obtained. The differential invariants of order 1 are constructed and the group classification are made starting from the equivalence algebra. At last some general class of variable coefficient nonlinear KdV-Burgers equations are mapped to constant-coefficient Burgers equation, KdV equation and KdV-Burgers equation. In particular, some exact solutions of the variable coefficients KdV-Burgers equation are obtained. |
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| Keywords: | nonlinear equation Lie’s invariance infinitesimal criterion differential invariants group classification generalized KdV-Burgers equation with variable coefficierts |
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