| 构造非线性演化方程精确解的一个新方法 |
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| 引用本文： | 邱春,刁明军,徐兰兰,岳书波,赵静.构造非线性演化方程精确解的一个新方法[J].量子电子学报,2012,29(3):279-285. |
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| 作者姓名： | 邱春 刁明军 徐兰兰 岳书波 赵静 |
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| 作者单位： | 四川大学水力学与山区河流开发保护国家重点实验室, 四川 成都 610065 |
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| 摘 要： | 基于辅助方程提出一种求解非线性演化方程的一个新方法，该方法简单易行且具有一定的普适性，根据不同的参数可给出各种形式的精确解，从而有助于探索非线性方程的新解及其性质。并以mkdv方程为例，得到了其多组精确解，包括Jacobi椭圆函数解及Weierstrass椭圆函数解等，除涵盖了以往结果，还给出一些新解。
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| 关 键 词： | 非线性方程 精确解 辅助方程 mkdv方程 |
| 收稿时间： | 2011/6/7 |
| 修稿时间： | 2011-08-06 |
A new algebra method for constructing exact solutions of nonlinear evolution equations |
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| QIU Chun
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DIAO Ming-jun
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XU Lan-lan
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YUE Shu-bo
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ZHAO Jing.A new algebra method for constructing exact solutions of nonlinear evolution equations[J].Chinese Journal of Quantum Electronics,2012,29(3):279-285. |
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| Authors: | QIU Chun DIAO Ming-jun XU Lan-lan YUE Shu-bo ZHAO Jing |
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| Affiliation: | State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China |
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| Abstract: | A new algebra method for constructing exact solutions of nonlinear evolution equations is proposed based on the auxiliary equation.The method is simple and universal.It can give various types of exact solutions according to different parameters,which are helpful to seek more new exact solutions and explore properties of nonlinear evolution equations.Many kinds of explicit solutions including Jacobi,and Weierstrass elliptic function solutions are obtained,some of which are new. |
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| Keywords: | nonlinear equation exact solution auxiliary equation mKdV equation |
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