| （3+1）维广义KdV-Zakharov-Kuznetsev方程的对称、约化和精确解 |
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| 引用本文： | 于兴江.（3+1）维广义KdV-Zakharov-Kuznetsev方程的对称、约化和精确解[J].量子电子学报,2014,31(6):670-677. |
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| 作者姓名： | 于兴江 |
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| 作者单位： | 聊城大学数学科学学院，山东 聊城 252059 |
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| 摘 要： | 利用直接对称方法得到了广义KdV-Zakharov-Kuznetsev方程（简写为mKdV-ZK）的对称约化、精确解，其中包括椭圆函数解，幂级数解，艾米儿函数解等. 利用得到的对称，求出了该方程的守恒律.
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| 关 键 词： | 非线性方程 mKdV-ZK方程 直接对称法 相似约化 精确解 守恒律 |
| 收稿时间： | 2014-03-10 |
| 修稿时间： | 2014-03-19 |
Symmetries,reductions and exact solutions of KdV-Zakharov-Kuznetsev equation |
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| YU Xingjiang.Symmetries,reductions and exact solutions of KdV-Zakharov-Kuznetsev equation[J].Chinese Journal of Quantum Electronics,2014,31(6):670-677. |
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| Authors: | YU Xingjiang |
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| Affiliation: | School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China |
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| Abstract: | By applying a direct symmetry method, the symmetry reduction, group invariant solution and many new exact solutions of the modified KdV-Zakharov-Kuznetsev equation (mKdV-ZK for short) are obtained, which include Jacobi elliptic function solutions, hyperbolic function solutions, trigonometric function solutions and so on. The conservation laws are derived at last. |
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| Keywords: | nonlinear equation mKdV-ZK equation direct symmetry method symmetry reduction exact solution conservation laws |
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