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

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...

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Bibliographic Details
Published in:Nonlinear dynamics 2014-03, Vol.75 (4), p.701-708
Main Authors: Zuo, Da-Wei, Gao, Yi-Tian, Meng, Gao-Qing, Shen, Yu-Jia, Yu, Xin
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dependent variables
Dynamical Systems
Eigenvalues
Engineering
Korteweg-Devries equation
Mathematical analysis
Mechanical Engineering
Nonlinear dynamics
Nonlinear equations
Nonlinear phenomena
Original Paper
Plasmas
Plasmas (physics)
Solitary waves
Solitons
Transformations
Vibration
Wave propagation
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Summary: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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-013-1096-0