摘要
在这篇论文，我们把我们的焦点放在一个可变系数的第五顺序的 Korteweg-de Vries (fKdV ) 方程上，它拥有很多优秀性质并且具有物理、工程的领域里的当前的重要性。某些限制被得出，它确认如此的一个方程的 integrability。在那些限制下面，一些 integrable 性质被导出，例如宽松的对和 Darboux 转变。经由 Darboux 转变，它是以一种递归的方式产生解决方案的一个可实行的方法， one-solitonic 和 two-solitonic 解决方案被介绍，一些域里的这些 solitonic 结构的相关物理应用程序也被指出。
In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.
基金
The project supported by the Key Project of the Chinese Ministry of Education under Grant No.106033
the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024
Chinese Ministry of Education,the National Natural Science Foundation of China under Grant Nos.60772023 and 60372095
the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001
Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
关键词
变量系数
fKdV方程
解题方法
算法
variable-coefficient fifth-order Korteweg-de Vries equation, Lax pair, Darboux transformation,solitonic solutions, symbolic computation
