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Multi-soliton solutions for the three-coupled KdV equations engendered by the Neumann system

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Abstract

Korteweg–de Vries (KdV)-type equations describe certain nonlinear phenomena in fluids and plasmas. In this paper, three-coupled KdV equations corresponding to the Neumann system of the fourth-order eigenvalue problem is investigated. Through the dependent variable transformations, bilinear forms of such equations are obtained, from which the multi-soliton solutions are derived. Soliton propagation and interaction are analyzed: (1) Bell- and anti-bell-shaped solitons are found; (2) Among the soliton images, one depends on the sign of wave numbers k i ’s (i=1,2,3), while the others are independent of such a sign; (3) Interaction between two solitons and among three solitons are elastic, i.e., the amplitude and velocity of each soliton remain unvaried after the interaction except for the phase shift.

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Acknowledgements

We express our sincere thanks to all the members of our discussion group for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11272023, and by the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications).

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Authors and Affiliations

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

    Da-Wei Zuo, Yi-Tian Gao, Gao-Qing Meng, Yu-Jia Shen & Xin Yu

  2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Da-Wei Zuo

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  1. Da-Wei Zuo
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Correspondence to Yi-Tian Gao.

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Zuo, DW., Gao, YT., Meng, GQ. et al. Multi-soliton solutions for the three-coupled KdV equations engendered by the Neumann system. Nonlinear Dyn 75, 701–708 (2014). https://doi.org/10.1007/s11071-013-1096-0

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