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Multi-soliton solutions and a Bäcklund transformation for a generalized variable-coefficient higher-order nonlinear Schrödinger equation with symbolic computation

Author

Listed:
  • Meng, Xiang-Hua
  • Liu, Wen-Jun
  • Zhu, Hong-Wu
  • Zhang, Chun-Yi
  • Tian, Bo

Abstract

In this paper, by virtue of symbolic computation, the investigation is made on a generalized variable-coefficient higher-order nonlinear Schrödinger equation with varying higher-order effects and gain or loss, which can describe the femtosecond optical pulse propagation in a monomode dielectric waveguide. A modified dependent variable transformation is introduced into the bilinear method to transform such an equation into a variable-coefficient bilinear form. Based on the formal parameter expansion technique, the multi-soliton solutions of this equation are obtained through the bilinear form under sets of parametric constraints. A Bäcklund transformation in bilinear form is also obtained for the first time in this paper. Finally, discussions on the analytic soliton solutions are given and various propagation situations are illustrated.

Suggested Citation

  • Meng, Xiang-Hua & Liu, Wen-Jun & Zhu, Hong-Wu & Zhang, Chun-Yi & Tian, Bo, 2008. "Multi-soliton solutions and a Bäcklund transformation for a generalized variable-coefficient higher-order nonlinear Schrödinger equation with symbolic computation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 97-107.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:1:p:97-107
    DOI: 10.1016/j.physa.2007.08.028
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