Z. Naturforsch. 68a, 261 – 271 (2013)
On the Nth Iterated Darboux Transformation and Soliton Solutions of a Coherently-Coupled Nonlinear Schrödinger System
Tao Xu1, Ping-Ping Xin1, Yi Zhang1, and Juan Li2,3
1 College of Science, China University of Petroleum, Beijing, 102249, China
2 State Key Laboratory of Remote Sensing Science, Jointly Sponsored by the Institute of Remote Sensing Applications of Chinese Academy of Sciences, and Beijing Normal University, Beijing 100101, China
3 Demonstration Centre, Spaceborne Remote Sensing National Space Administration, Beijing 100101, China
Received June 8, 2012/ revised October 7, 2012 / published online February 6, 2013
Reprint requests to: T. X.; E-mail: xutao@cup.edu.cn
In this paper, we study an integrable coherently-coupled nonlinear Schrödinger system arising from low birefringent fibers and weakly anisotropic media. We construct the Nth iterated Darboux transformation (DT) in the explicit form and give a complete proof for the gauge equivalence of the associated Lax pair. By the DT-based algorithm, we derive the N-soliton solutions which can be uniformly represented in terms of the four-component Wronskians. We analyze the properties of coherently coupled solitons, revealing the parametric criterion for the non-degenerate solitons to respectively display the one- and double-hump profiles. In addition, we point out that the double-hump solitons may have potential application in realizing the multi-level optical communication.
Key words: Coherently-Coupled Nonlinear Schrödinger System; Darboux Transformation; Soliton Solutions; Four-Component Wronskians.
PACS numbers: 05.45.Yv; 02.30.Ik
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