| 三Riccati 方程的新展开法及其在非线性数学物理方程中的应用 |
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| 引用本文： | 智红燕,赵雪芹,张鸿庆.三Riccati 方程的新展开法及其在非线性数学物理方程中的应用[J].中国物理 B,2005,14(7):1296-1302. |
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| 作者姓名： | 智红燕 赵雪芹 张鸿庆 |
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| 作者单位： | Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Department of Mathematics, Qufu Normal University, Qufu 273165, China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; |
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| 摘 要： | 通过对tanh函数法和射影Riccati方程法的探讨, 提出一种新的算法来求解非线性发展方程. 并且通过求解高阶 schrodinger 方程和 mKdV 方程来说明该算法.得到了这些方程的新形式解,包括新的孤立波解, 周期解等, 并图示一些新形式解.
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| 关 键 词： | 符号计算 孤立波解 周期解 高阶 schrodinger 方程 mKdV 方程 |
| 收稿时间： | 2004-12-30 |
New expansion algorithm of three Riccati equations and its applications in nonlinear mathematical physics equations |
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| Zhi Hong-Yan,Zhao Xue-Qin and Zhang Hong-Qing.New expansion algorithm of three Riccati equations and its applications in nonlinear mathematical physics equations[J].Chinese Physics B,2005,14(7):1296-1302. |
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| Authors: | Zhi Hong-Yan Zhao Xue-Qin and Zhang Hong-Qing |
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| Institution: | Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;; Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Department of Mathematics, Qufu Normal University, Qufu 273165, China |
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| Abstract: | Based on the study of tanh function method and the coupled projective Riccati equation method, we propose a new algorithm to search for explicit exact solutions of nonlinear evolution equations. We use the higher-order Schr\"{o}dinger equation and mKdV equation to illustrate this algorithm. As a result, more new solutions are obtained, which include new solitary solutions, periodic solutions, and singular solutions.Some new solutions are illustrated in figures. |
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| Keywords: | symbolic computation solitary wave solution periodic solution higher-order Schr\"{o}dinger equation mKdV equation |
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