Journal
NONLINEAR DYNAMICS
Volume 66, Issue 1-2, Pages 161-168Publisher
SPRINGER
DOI: 10.1007/s11071-010-9918-9
Keywords
(1+1)-dimensional nonlinear dispersive-wave system; Shallow water; Soliton shape preserving; Soliton complex; Darboux transformation; Symbolic computation
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Funding
- National Natural Science Foundation of China [60772023]
- State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics [BUAA-SKLSDE-09KF-04, SKLSDE-2010ZX-07]
- National Basic Research Program of China (973 Program) [2005CB321901]
- Chinese Ministry of Education [200800130006]
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Under investigation in this paper is a (1+1)-dimensional nonlinear dispersive-wave system for the long gravity waves in shallow water. With symbolic computation, we derive the multi-soliton solutions for the system. Four sorts of interactions for the system are discussed: (1) Soliton shape preserving, in which two solitons undergo the fusion behavior while the amplitudes and velocities of the other two remain unchanged during the interaction process; (2) Head-on collisions between the two-soliton complexes; (3) Overtaking collisions between the two-soliton complexes; (4) Two-soliton complexes formed by the inelastic collisions. Such soliton structures might be of certain value in fluid dynamics.
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