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Soliton-shape-preserving and soliton-complex interactions for a (1+1)-dimensional nonlinear dispersive-wave system in shallow water

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Abstract

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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Authors and Affiliations

  1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Bei**g University of Aeronautics and Astronautics, Bei**g, 100191, China

    Lei Wang, Yi-Tian Gao, De-**n Meng, **ao-Ling Gai & Peng-Bo Xu

  2. State Key Laboratory of Software Development Environment, Bei**g University of Aeronautics and Astronautics, Bei**g, 100191, China

    Yi-Tian Gao

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  1. Lei Wang
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Correspondence to Yi-Tian Gao.

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Wang, L., Gao, YT., Meng, DX. et al. Soliton-shape-preserving and soliton-complex interactions for a (1+1)-dimensional nonlinear dispersive-wave system in shallow water. Nonlinear Dyn 66, 161–168 (2011). https://doi.org/10.1007/s11071-010-9918-9

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