| Symmetry Reduction, Exact Solutions, and Conservation Laws of （2＋1）-Dimensional Burgers Korteweg-de Vries Equation |
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| 作者姓名： | DONG Zhong-Zhou LIU Xi-Qiang BAI Cheng-Lin |
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| 作者单位： | [1]School of Mathematical Science, Liaocheng University, Liaocheng 252059, China [2]School of Physical Science and Information Engineering, Liaocheng University, Liaocheng 252059, China |
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| 基金项目： | The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx 16 |
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| 摘 要： | Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.
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| 关 键 词： | 3维BKdV方程 守恒法则 无穷小量 精确解 |
| 收稿时间： | 2005-08-26 |
| 修稿时间： | 2005-08-26 |
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