Exact multisoliton solutions of the higher-order nonlinear Schrödinger equation with variable coefficients

Ruiyu Hao, Lu Li, Zhonghao Li, and Guosheng Zhou
Phys. Rev. E 70, 066603 – Published 3 December 2004
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Abstract

We investigate the generalized higher-order nonlinear Schrödinger equation with variable coefficients under two sets of parametric conditions. The exact one-soliton solution is presented by the ansatz method for one set of parametric conditions. For the other, exact multisoliton solutions are presented by employing the Darboux transformation based on the Lax pair. As an example, we consider a soliton control system, and the results show that the soliton control system may relax the limitations to parametric conditions. The stability of the solution is discussed numerically; the results reveal that finite initial perturbations, such as amplitude, chirp, or white noise, could not influence the main character of the solution. In addition, the evolution of a quite arbitrary Gaussian pulse and the interaction between neighboring pulses have been studied in detail.

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  • Received 22 December 2003

DOI:https://doi.org/10.1103/PhysRevE.70.066603

©2004 American Physical Society

Authors & Affiliations

Ruiyu Hao1,3,4, Lu Li2,4,*, Zhonghao Li1,4, and Guosheng Zhou1,4,†

  • 1Department of Electronics and Information Technology, Shanxi University, Taiyuan 030006, China
  • 2Department of Physics, and Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
  • 3State Key Laboratory of Quantum Optics and Quantum Optics Devices, Taiyuan 030006, China
  • 4The State Key Subject of Optics, Shanxi University, Taiyuan 030006, China

  • *Corresponding author. Electronic address: llz@sxu.edu.cn
  • †Corresponding author. Electronic address: zhougs@sxu.edu.cn

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Vol. 70, Iss. 6 — December 2004

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