| 含外力项时变系数KdV方程与时变系数耦合KdV方程组的孤子解 |
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| 引用本文： | 杨绍杰,化存才.含外力项时变系数KdV方程与时变系数耦合KdV方程组的孤子解[J].动力学与控制学报,2014,12(2):115-118. |
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| 作者姓名： | 杨绍杰 化存才 |
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| 作者单位： | 云南师范大学数学学院, 昆明 650500;云南师范大学数学学院, 昆明 650500 |
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| 基金项目： | 国家自然科学基金资助项目(11162020)、云南省中青年学术与技术带头人计划项目(2008PY059) |
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| 摘 要： | 应用孤子拟解法研究了含外力项时变系数KdV方程与一类时变系数耦合KdV方程组.首先将方程经过变量代换转换为齐次方程,然后将孤子解假设为双曲正割函数的形式带入方程或方程组,最后借助Maple软件完成复杂的计算来确定假设的孤子解的待定系数,从而得到孤子解存在的条件及其孤子解.结果显示:孤子拟解法计算简便且能得到方程的亮孤子解.
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| 关 键 词： | KdV方程 耦合KdV方程组 变系数 孤子拟解法 |
Soliton solutions of KDV equation and a coupled KDV equation with time dependent coefficients and forcing term |
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| Yang Shaojie and Hua Cuncai.Soliton solutions of KDV equation and a coupled KDV equation with time dependent coefficients and forcing term[J].Journal of Dynamics and Control,2014,12(2):115-118. |
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| Authors: | Yang Shaojie and Hua Cuncai |
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| Affiliation: | ( School of Mathematics, Yunnan Normal University, Kunming 650500, China) |
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| Abstract: | This paper studied the KdV equation with time dependent coefficients and forcing term and the coupled KdV equations with time dependent coefficients by using soliton ansaze. Firstly, the equation was converted to homogeneous equation by using a variable transformation. Then, by assuming the soliton solutions to be the form of sech function, and with the help of Maple software, the complicated and tedious calculations were performed, and the conditions of existence of solitons and soliton solutions were obtained. The results show that the calculation of soliton ansaze is simple and can obtain bright soliton solutions. |
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| Keywords: | KdV equation coupled KdV equations time-dependent coefficients soliton ansatz |
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