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

İSKENDEROĞLU G., KAYA D.

Chaos, Solitons and Fractals, cilt.162, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 162
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.chaos.2022.112453
  • Dergi Adı: Chaos, Solitons and Fractals
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Anahtar Kelimeler: Lie groups, Nonlinear Schro ?dinger equations, Self -similar solutions
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

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.