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Stable propagation of optical solitons for nonlinear Schrödinger equation with dispersion and self phase modulation

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  • Rizvi, Syed Tahir Raza
  • Khan, Salah Ud-Din
  • Hassan, Mohsan
  • Fatima, Ishrat
  • Khan, Shahab Ud-Din

Abstract

In this paper, we study modulated compressional dispersive Alfvén (MCDA) waves with group velocity dispersion (GVD) and self-phase modulation (SPM) for multiple soliton interaction using Hirota bilinear method (HBM). We have obtained one, two and three soliton solutions. By choosing λ1(t), λ2(t) and λ3(t) as different functions and we have observed parabolic, bright, M-shaped and S-shaped anti dark solitons. The obtained results might be significant to study optical logic switches and ultrashort pulse lasers.

Suggested Citation

  • Rizvi, Syed Tahir Raza & Khan, Salah Ud-Din & Hassan, Mohsan & Fatima, Ishrat & Khan, Shahab Ud-Din, 2021. "Stable propagation of optical solitons for nonlinear Schrödinger equation with dispersion and self phase modulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 126-136.
    • Handle: RePEc:eee:matcom:v:179:y:2021:i:c:p:126-136
    DOI: 10.1016/j.matcom.2020.08.014
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    References listed on IDEAS

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    1. Osman, M.S. & Wazwaz, Abdul-Majid, 2018. "An efficient algorithm to construct multi-soliton rational solutions of the (2+ 1)-dimensional KdV equation with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 282-289.
    2. Liu, Wenjun & Zhang, Yujia & Wazwaz, Abdul Majid & Zhou, Qin, 2019. "Analytic study on triple-S, triple-triangle structure interactions for solitons in inhomogeneous multi-mode fiber," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 325-331.
    3. Lu, Changna & Fu, Chen & Yang, Hongwei, 2018. "Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 104-116.
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    Cited by:

    1. Mann, Nikita & Rani, Setu & Kumar, Sachin & Kumar, Raj, 2024. "Novel closed-form analytical solutions and modulation instability spectrum induced by the Salerno equation describing nonlinear discrete electrical lattice via symbolic computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 473-490.
    2. Cheng, Li & Zhang, Yi & Ma, Wen-Xiu & Ge, Jian-Ya, 2021. "Wronskian and lump wave solutions to an extended second KP equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 720-731.
    3. Rizvi, Syed T.R. & Seadawy, Aly R. & Farah, N. & Ahmad, S., 2022. "Application of Hirota operators for controlling soliton interactions for Bose-Einstien condensate and quintic derivative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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