Multi-soliton solutions for a higher-order coupled nonlinear Schrödinger system in an optical fiber via Riemann–Hilbert approach

Abstract

The main objective of this work is to study the multi-soliton solutions for the higher-order coupled nonlinear Schrödinger system in an optical fiber. Firstly, by using the Riemann–Hilbert (RH) approach as well as analyzing the related spectral problem of the Lax pair, a matrix RH problem for the system is strictly formulated. Secondly, a series of multi-soliton solutions including breathers and interaction solutions can be computed from the RH problem with the reflectionless case. Thirdly, the propagation and collision dynamic behaviors as well as localized wave characteristics of these solutions are presented by selecting appropriate parameters with some graphics. The innovation and highlights of this article are shown through obtained interesting results. The one is that the higher-order linear and nonlinear term \(\varepsilon \) has important impact on the velocity, phase, period, and wavewidth of wave dynamics. The other is that collisions for the second-order breathers and soliton solutions are elastic interaction which imply they remain bounded all the time. Nevertheless, third-order breathers and soliton solutions are inelastic interaction and the amplitude decreases rapidly with time when collisions occur.

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Acknowledgements

We would like to express our sincere thanks to editor and reviewers for their valuable comments on this paper. The work was supported in part by the National Natural Science Foundation of China under Grant No. 11975145.

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Correspondence to Han-Dong Guo or Tie-Cheng Xia.

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Guo, HD., Xia, TC. Multi-soliton solutions for a higher-order coupled nonlinear Schrödinger system in an optical fiber via Riemann–Hilbert approach. Nonlinear Dyn 103, 1805–1816 (2021). https://doi.org/10.1007/s11071-020-06166-5

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Keywords

  • Riemann–Hilbert approach
  • Spectral analysis
  • Higher-order coupled nonlinear Schrödinger system
  • Breathers
  • Soliton solutions