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Z. Naturforsch. 67a, 39 – 49 (2012)
doi:10.5560/ZNA.2011-0055
Bright N-Soliton Solutions to the Vector Hirota Equation from Nonlinear Optics with Symbolic Computation
Tao Xu1,2, Bo Tian1,2,3, and Feng-Hua Qi1,2
1 State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
2 School of Science, P. O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China
3 State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
Received March 9, 2011 / revised July 17, 2011
Reprint requests to: B. T.; E-mail: tian.bupt@yahoo.com.cn
Under investigation in this paper is the vector Hirota (VH) equation which governs the simultaneous propagation of multiple interacting femtosecond pulses in a certain type of coupled optical waveguides. By the Nth iterated Darboux transformation starting from the zero potential, the VH equation is found to admit the bright N-soliton solutions in terms of the multi-component Wronskian. Asymptotic formulae of the bright N-soliton solutions are derived for any given set of spectral parameters, which allows us to directly analyze the collision dynamics of VH solitons. Via symbolic computation, some collision properties possessed by the two- and three-soliton solutions are revealed from four aspects: the asymptotic patterns of the colliding solitons, parametric conditions for the amplitude-preserving collisions, phase shifts induced by the vector-soliton collisions, and soliton state changes described by the generalized linear fractional transformations.
Key words: Vector Solitons; Vector Hirota Equation; Multi-Component Wronskian; Darboux Transformation; Symbolic Computation.
PACS numbers: 05.45.Yv; 02.30.Ik
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