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Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method

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  • Iskenderoglu, Gulistan
  • Kaya, Dogan

Abstract

In this work, we present an application of Lie group analysis to study the generalized derivative nonlinear Schrödinger equation, which governs the evolution of a nonlinear wave and plays an important role in the propagation of short pulses in optical fiber systems. To construct Lie group reductions, we study the symmetry properties and introduce various infinitesimal operators. Further, we obtain self-similar solutions and periodic soliton solutions of the generalized derivative nonlinear Schrödinger equation. This type of solution plays a vital role in the study of the blow-up and asymptotic behavior of non-global solutions. And at the end, we present graphs for each solution by considering the physical meaning of the solutions.

Suggested Citation

  • Iskenderoglu, Gulistan & Kaya, Dogan, 2022. "Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006634
    DOI: 10.1016/j.chaos.2022.112453
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    References listed on IDEAS

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    1. Daoui, Abdel Kader & Messouber, Abdelouahab & Triki, Houria & Zhou, Qin & Biswas, Anjan & Liu, Wenjun & Alzahrani, Abdullah K. & Belic, Milivoj R., 2021. "Propagation of chirped periodic and localized waves with higher-order effects through optical fibers," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Kumar, Sachin & Malik, Sandeep & Biswas, Anjan, 2020. "A re-visitation to reported results on optical solitons," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
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    Cited by:

    1. Wang, S.-F., 2024. "Spatial optical soliton cluster solutions in strongly nonlocal nonlinear media," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Rosa, M. & Gandarias, M.L. & Niño-López, A. & Chulián, S., 2023. "Exact solutions through symmetry reductions for a high-grade brain tumor model with response to hypoxia," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Rafiq, Muhammad Hamza & Raza, Nauman & Jhangeer, Adil & Zidan, Ahmed M., 2024. "Qualitative analysis, exact solutions and symmetry reduction for a generalized (2＋1)-dimensional KP–MEW-Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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