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Z. Naturforsch. 67a, 711 – 722 (2012)
doi:10.5560/ZNA.2012-0084
Darboux Transformation and N-Soliton Solution for the Coupled Modified Nonlinear Schrödinger Equations
Hai-Qiang Zhang
College of Science, P. O. Box 253, University of Shanghai for Science and Technology, Shanghai 200093, China
Received May 4, 2012 / revised August 14, 2012 / published online November 14, 2012
Reprint requests to: H. Z.; E-mail: zhanghqbupt@yahoo.com.cn
The pulse propagation in the picosecond or femtosecond regime of birefringent optical fibers is governed by the coupled mixed derivative nonlinear Schrödinger (CMDNLS) equations. A new type of Lax pair associated with such coupled equations is derived from the Wadati–Konno–Ichikawa spectral problem. The Darboux transformation method is applied to this integrable model, and the N-times iteration formula of the Darboux transformation is presented in terms of the compact determinant representation. Starting from the zero potential, the bright vector N-soliton solution of CMDNLS equations is expressed as a compact determinant by N complex eigenvalues and N linearly independent eigenfunctions. The collision mechanisms in two components shows that bright vector solitons can exhibit the standard elastic and inelastic collisions. Such energy-exchange collision behaviours have potential applications in the construction of logical gates, the design of fiber directional couplers, and quantum information processors.
Key words: Coupled Mixed Derivative Nonlinear Schrödinger Equations; Vector Soliton; Soliton Collision; Darboux Transformation.
PACS numbers: 05.45.Yv; 42.65.Tg; 42.81.Dp
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