摘要
In this paper, two types of the （2＋1）-dimensional breaking soliton equations axe investigated, which describe the interactions of the Riemann waves with the long waves. With symbolic computation, the Hirota bilineax forms and Bgcklund transformations are derived for those two systems. Furthermore, multisoliton solutions in terms of the Wronskian determinant are constructed, which are verified through the direct substitution of the solutions into the bilineax equations. Via the Wronskian technique, it is proved that the Bgcklund transformations obtained are the ones between the （ N - 1）- and N-soliton solutions. Propagations and interactions of the kink-/bell-shaped solitons are presented. It is shown that the Riemann waves possess the solitonie properties, and maintain the amplitudes and velocities in the collisions only with some phase shifts.
基金
Supported by the National Natural Science Foundation of China under Grant No.60772023
the Open Fund under Grant No.BUAASKLSDE-09KF-04l
Supported Project under Grant No.SKLSDE-2010ZX-07 of the State Key Laboratory of Software Development Environment,Beijing University of Aeronautics and Astronautics
the National Basic Research Program of China (973 Program) under Grant No.2005CB321901
the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.200800130006,Chinese Ministry of Education
