| A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations |
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| 引用本文： | ZHAO Xue-Qin ZHI Hong-Yan. A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations[J]. 理论物理通讯, 2007, 48(5): 781-786 |
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| 作者姓名： | ZHAO Xue-Qin ZHI Hong-Yan |
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| 作者单位： | [1]Department of Mathematics, Qufu Normal University, Rizhao 276826, China [2]Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China |
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| 基金项目： | The project supported by National Natural Science Foundation of China under Grant Nos. 10474118 and 10274093, the National Fundamental Research Program of China under Grant No. 2005CB724502, and the Foundation from Educational Department of Sichuan Province of China under Grant No. 2004C017 |
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| 摘 要： | A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
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| 关 键 词： | 代数方法 非线性进化方程式 独立波 物理学 |
| 修稿时间： | 2006-06-14 |
A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations |
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| FAN Yun-Xia,LIU Tao,FENG Mang,WANG Ke-Lin,. A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations[J]. Communications in Theoretical Physics, 2007, 48(5): 781-786 |
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| Authors: | FAN Yun-Xia LIU Tao FENG Mang WANG Ke-Lin |
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| Abstract: | The Jaynes-Cummings model (JCM) is studied in the absence of the rotating-wave approximation (RWA)by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers. |
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| Keywords: | new general algebraic method nonlinear evolution equations solitary wave solutions |
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