| 第二类变系数KdV方程的新类型无穷序列精确解 |
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| 引用本文： | 套格图桑,白玉梅.第二类变系数KdV方程的新类型无穷序列精确解[J].物理学报,2012,61(6):60201-060201. |
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| 作者姓名： | 套格图桑 白玉梅 |
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| 作者单位： | 内蒙古民族大学数学学院, 通辽 028043;内蒙古师范大学数学科学学院, 呼和浩特 010022;内蒙古民族大学数学学院, 通辽 028043 |
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| 基金项目： | 国家自然科学基金(批准号:10862003)、内蒙古自治区高等学校科学研究基金(批准号:NJZZ07031)和内蒙古自治区自然科学基金(批准号:2010MS0111)资助的课题. |
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| 摘 要： | 为了构造变系数非线性发展方程的无穷序列新精确解, 发掘第一种椭圆辅助方程的构造性和机械化性特点, 获得了该方程的 新类型解和相应的 Bäcklund 变换. 在符号计算系统 Mathematica 的帮助下, 以第二类变系数 KdV 方程为应用实例, 构造了三种类型的无穷序列新精确解. 这里包括无穷序列光滑类孤子解、无穷序列尖峰孤立子解和无穷序列紧孤立子解. 这种方法也可以获得其他变系数非线性发展方程的无穷序列新精确解.
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| 关 键 词： | 第一种椭圆辅助方程 Bäcklund 变换 变系数非线性发展方程 无穷序列新精确解 |
| 收稿时间： | 2011-05-24 |
New type infinite sequence exact solutions of the second KdV equation with variable coefficients |
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| Taogetusang and Bai Yu-Mei.New type infinite sequence exact solutions of the second KdV equation with variable coefficients[J].Acta Physica Sinica,2012,61(6):60201-060201. |
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| Authors: | Taogetusang and Bai Yu-Mei |
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| Institution: | The College of Mathematical, Inner Mongolia University for Nationalities, Tongliao 028043, China;The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China;The College of Mathematical, Inner Mongolia University for Nationalities, Tongliao 028043, China |
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| Abstract: | To construct a number of new infinite sequence exact solutions of nonlinear evolution equations and to study the two characteristics of constructivity and mechanicalness of the first kind of elliptic equation, new types of solutions and the corresponding Bäcklund transformation of the equation are presented. Then the second kind of KdV equation with variable coefficients is chosen as a practical example and three kinds of new infinite sequence exact solutions are obtained with the help of symbolic computation system Mathematica, where are included the smooth soliton-like solutions, the infinite sequence peak soliton solutions, and the infinite sequence compact soliton solutions. The method can be used to search for new infinite sequence exact solutions of other nonlinear evolution equations with variable coefficients. |
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| Keywords: | the first kind of elliptic equation Bäcklund transformation nonlinear evolution equation with variable coefficients new infinite sequence exact solutions |
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