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Nonlinear Dynamics

, Volume 78, Issue 1, pp 755–770 | Cite as

Soliton interactions for coupled nonlinear Schrödinger equations with symbolic computation

  • Wen-Jun Liu
  • Nan Pan
  • Long-Gang Huang
  • Ming Lei
Original Paper

Abstract

Soliton interactions for the coupled nonlinear Schrödinger equations, governing the propagation of envelopes of electromagnetic waves in birefringent optical fibers, are investigated with symbolic computation. Based on the Hirota method, analytic two- and three-soliton solutions for this model are derived. Relevant interaction properties are discussed. Stationary bound vector solitons with the periodic attraction and repulsion are obtained. Soliton intensity could be reduced if the nonlinearity in optical fibers is enlarged, while the soliton period could be prolonged as the group velocity dispersion in the anomalous dispersion regime of optical fibers increases. Through the asymptotic analysis for the two-soliton solutions, interactions between two solitons are proven to be elastic. Besides, parallel soliton transmission systems without soliton interactions are presented. Moreover, interactions between the regular and bound vector solitons are studied. Dual complex structures and triple-soliton bound states are presented. Results could be of certain value to the studies on the soliton control and optical switching technologies.

Keywords

Coupled nonlinear Schrödinger equations Symbolic computation Soliton solution Bound vector solitons Soliton interactions 

Notes

Acknowledgments

We express our sincere thanks to the Editors and Referees for their valuable comments. This work has been supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 61205064), by the Visiting Scholar Funds of the Key Laboratory of Optoelectronic Technology & Systems under Grant No. \(0902011812401_{-}5\), Chongqing University.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Wen-Jun Liu
    • 1
  • Nan Pan
    • 1
  • Long-Gang Huang
    • 1
  • Ming Lei
    • 1
  1. 1.State Key Laboratory of Information Photonics and Optical CommunicationsSchool of Science, Beijing University of Posts and TelecommunicationsBeijingChina

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