摘要
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
