Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method. (September 2022)

• Record Type: Journal Article
• Authors: Iskenderoglu, Gulistan; Kaya, Dogan
• Is Part Of: Chaos, solitons and fractals. Volume 162(2022)
• Publication Date: 2022-09
• Subjects: Lie groups -- Nonlinear Schrödinger equations -- Self-similar solutions; 70G65 -- 35Q55 -- 35C06; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112453
• Languages: English
• ISSNs: 0960-0779

Abstract

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. Highlights: An application of the Lie group analysis to study the gDNLS equations was presented. The self-similar solutions and envelope periodic wave solutions of the DNLS equation were obtained. By giving the graphs for each solution, the physical meaning of the obtained solutions was consider.