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Envelope bright- and dark-soliton solutions for the Gerdjikov–Ivanov model

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Abstract

Within the context of the Madelung fluid description, investigation has been carried out on the connection between the envelope soliton-like solutions of a wide family of nonlinear Schrödinger equations and the soliton-like solutions of a wide family of Korteweg–de Vries or Korteweg–de Vries-type equations. Under suitable hypothesis for the current velocity, the Gerdjikov–Ivanov envelope solitons are derived and discussed in this paper. For a motion with the stationary profile current velocity, the fluid density satisfies a generalized stationary Gardner equation, which possesses bright- and dark-type (including gray and black) solitary waves due to associated parametric constraints, and finally envelope solitons are found correspondingly for the Gerdjikov–Ivanov model. Moreover, this approach may be useful for studying other nonlinear Schrödinger-type equations.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No. 61308018, by China Postdoctoral Science Foundation under Grant No. 2014T70031, by the Fundamental Research Funds for the Central Universities of China (2014RC019 and 2015JBM111). WXM is supported in part by the National Natural Science Foundation of China under Grant Nos. 11271008 and 11371326, Natural Science Foundation of Shanghai under Grant No. 11ZR1414100, Zhejiang Innovation Project of China under Grant No. T200905, the First-class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project (No. A13-0101-12-004) and Shanghai University of Electric Power.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiao Tong University, Beijing, 100044, China

    Xing Lü

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Xing Lü, Wen-Xiu Ma & Jun Yu

  3. Institute of Nonlinear Science, Shaoxing University, Shaoxing, 312000, China

    Jun Yu

  4. School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Fuhong Lin

  5. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, South Africa

    Chaudry Masood Khalique

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  1. Xing Lü
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  2. Wen-Xiu Ma
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Correspondence to Xing Lü.

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Lü, X., Ma, WX., Yu, J. et al. Envelope bright- and dark-soliton solutions for the Gerdjikov–Ivanov model. Nonlinear Dyn 82, 1211–1220 (2015). https://doi.org/10.1007/s11071-015-2227-6

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  • DOI: https://doi.org/10.1007/s11071-015-2227-6

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