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Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium

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  • Shen, Yuan
  • Tian, Bo
  • Zhou, Tian-Yu
  • Cheng, Chong-Dong

Abstract

Investigations on nonlinear optics are active, with the applications in the modulators, fiber lasers, optical sensors, etc. In this paper, we focus our attention on a system for the ultra-short pulses in an inhomogeneous multi-component nonlinear optical medium. Starting from the existing Lax pair and one-fold Darboux transformation (DT), we construct the N-fold DT of that system, which involves N distinct spectral parameters, where N is a positive integer. The N-fold generalized DT with one spectral parameter is obtained through resorting to the Taylor-series-expansion coefficients of a special solution to that Lax pair. Double-pole soliton solutions of that system are derived via that N-fold generalized DT with N=2. With the aid of the N-fold DT, an N-fold Darboux matrix is constructed, based on which the multi-pole soliton solutions in the determinant form with respect to the electromagnetic field E are determined. Graphically, we find that those double-pole soliton solutions are a kind of the bound-state soliton solutions which represent the elastic interactions between the two solitons. Effects of the coefficients in that system on the double-pole soliton are shown via choosing the trigonometric, linear and quadratic functions. Furthermore, we present the triple-pole soliton and quadruple-pole soliton with respect to E. Our results might be useful in understanding the ultra-short pulses in the nonlinear optical media.

Suggested Citation

  • Shen, Yuan & Tian, Bo & Zhou, Tian-Yu & Cheng, Chong-Dong, 2023. "Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
  • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003983
    DOI: 10.1016/j.chaos.2023.113497
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    References listed on IDEAS

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    1. Yang, Dan-Yu & Tian, Bo & Tian, He-Yuan & Wei, Cheng-Cheng & Shan, Wen-Rui & Jiang, Yan, 2022. "Darboux transformation, localized waves and conservation laws for an M-coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Bel, G. & Alexandrov, B.S. & Bishop, A.R. & Rasmussen, K.Ø., 2023. "Patterns and stability of coupled multi-stable nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. S. Saha Ray & Shailendra Singh, 2022. "New bright soliton solutions for Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equations and bidirectional propagation of water wave surface," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-15, May.
    4. Dzyubak, Larysa & Dzyubak, Oleksandr & Awrejcewicz, Jan, 2023. "Nonlinear multiscale diffusion cancer invasion model with memory of states," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    5. Wu, Xi-Hu & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui, 2022. "N-fold generalized Darboux transformation and soliton interactions for a three-wave resonant interaction system in a weakly nonlinear dispersive medium," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
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    Cited by:

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