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 bilinea...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.展开更多
Gibbilimbols B and D were synthesized from the facile rearrangement of sulfone in the presence of dibromodifluoromethane and alumina-supported KOH in dichloromethane, followed by refluxing the rearrangement products i...Gibbilimbols B and D were synthesized from the facile rearrangement of sulfone in the presence of dibromodifluoromethane and alumina-supported KOH in dichloromethane, followed by refluxing the rearrangement products in conc. HCI and methanol and then treating with thiophenol in the presence of AIBN.展开更多
We modify the bilinear Biicklund transformation for the discrete sine-Gordon equation and derive variety of solutions by freely choosing parameters from the modified B^cklund transformation. Dynamics of solutions and ...We modify the bilinear Biicklund transformation for the discrete sine-Gordon equation and derive variety of solutions by freely choosing parameters from the modified B^cklund transformation. Dynamics of solutions and continuum limits are also discussed.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.60772023 the Open Fund under Grant No.BUAASKLSDE-09KF-04l+2 种基金Supported Project under Grant No.SKLSDE-2010ZX-07 of the State Key Laboratory of Software Development Environment,Beijing University of Aeronautics and Astronauticsthe 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
文摘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Project supported by the National Basic Research Program(973 Program)of Chinathe National Natural Science Foundation of China(Nos.2007CB108903 and 20621091).
文摘Gibbilimbols B and D were synthesized from the facile rearrangement of sulfone in the presence of dibromodifluoromethane and alumina-supported KOH in dichloromethane, followed by refluxing the rearrangement products in conc. HCI and methanol and then treating with thiophenol in the presence of AIBN.
基金Supported by the National Natural Science Foundation of China under Grant No.10671121Shanghai Leading Academic Discipline Project under Grant No.J50101
文摘We modify the bilinear Biicklund transformation for the discrete sine-Gordon equation and derive variety of solutions by freely choosing parameters from the modified B^cklund transformation. Dynamics of solutions and continuum limits are also discussed.
