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Discrete bright soliton solutions and modulation instability for the nonlocal semi-discrete nonlinear Schrödinger equation

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  • Qin, Qing
  • Li, Li
  • Yu, Fajun

Abstract

The nonlocal semi-discrete nonlinear Schrödinger equation (SD-NLSE) has significant theoretical value, and it can describe the propagation of nonlinear wave. By applying Hirota’s bilinear method and constructing appropriate transformations, we successfully obtain the analytical expressions of discrete bright soliton solutions and elaborate on their propagation characteristics. At the same time, we present the image analysis of discrete bright soliton solutions via selecting different parameters, and find that the discrete soliton solutions exhibit periodic oscillatory behaviors. To further illustrate the relevant properties of the obtained solutions, we discuss the modulation instability (MI) of discrete bright one-soliton solution. Most researchers use the Hirota’s bilinear method to study the continuous local nonlinear Schrödinger equation. However, we investigate the nonlocal semi-discrete equation. We use the extended bilinear method to study the nonlocal SD-NLSE and conduct stability analysis by increasing a small perturbation. The obtained results are novel, which confirm the applicability of the extended bilinear method to the nonlocal semi-discrete equations. The results not only enrich the soliton theory of nonlocal semi-discrete systems, but also provide ideas for experiments of related physical problems.

Suggested Citation

  • Qin, Qing & Li, Li & Yu, Fajun, 2025. "Discrete bright soliton solutions and modulation instability for the nonlocal semi-discrete nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012196
    DOI: 10.1016/j.chaos.2025.117206
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    References listed on IDEAS

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    1. Qin, Qing & Li, Li & Yu, Fajun, 2025. "Dark matter-wave bound soliton molecules and modulation stability for spin-1 Gross–Pitaevskii equations in Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    2. Aly R. Seadawy, 2017. "Modulation instability analysis for the generalized derivative higher order nonlinear Schrödinger equation and its the bright and dark soliton solutions," Journal of Electromagnetic Waves and Applications, Taylor & Francis Journals, vol. 31(14), pages 1353-1362, September.
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