Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality

This study investigated the dynamics of a pure-quartic nonlinear Schrödinger equation incorporating a $ \beta $-fractional derivative and weak nonlocal effects prevalent in optical fiber systems. Using the improved modified extended tanh-function method, we obtained a diverse array of soliton soluti...

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Veröffentlicht in:AIMS mathematics Jg. 10; H. 3; S. 7489 - 7508
Hauptverfasser: Soliman, Mahmoud, Ahmed, Hamdy M., Badra, Niveen, Ramadan, M. Elsaid, Samir, Islam, Alkhatib, Soliman
Format: Journal Article
Sprache:Englisch
Veröffentlicht: AIMS Press 01.03.2025
Schlagworte:
fractional derivatives
improved modified extended tanh-function method
nonlinear schrödinger equation
soliton solutions
ISSN:2473-6988, 2473-6988
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Abstract This study investigated the dynamics of a pure-quartic nonlinear Schrödinger equation incorporating a $ \beta $-fractional derivative and weak nonlocal effects prevalent in optical fiber systems. Using the improved modified extended tanh-function method, we obtained a diverse array of soliton solutions, including bright, dark, and singular solitons, as well as hyperbolic, trigonometric, and Jacobi elliptic solutions. The main goal was to clarify how fractional derivatives, defined by the parameter $ \beta $, affect the characteristics and behavior of these soliton solutions. The key outcomes indicate that variations in the parameter $ \beta $ lead to substantial changes in soliton amplitude, shape, and propagation patterns. Graphical illustrations clearly depict these transformations, highlighting how fractional derivatives have a major impact on the properties of solitons. Crucially, for certain fractional orders, the localization and stability of solitons are enhanced, which is essential for accurate modeling of nonlocal and dispersive effects in optical fibers. This work not only enhances fundamental understanding of nonlinear wave phenomena within optical communication systems but also offers valuable insights into using fractional calculus for designing and optimizing advanced photonic devices.
AbstractList This study investigated the dynamics of a pure-quartic nonlinear Schrödinger equation incorporating a $ \beta $-fractional derivative and weak nonlocal effects prevalent in optical fiber systems. Using the improved modified extended tanh-function method, we obtained a diverse array of soliton solutions, including bright, dark, and singular solitons, as well as hyperbolic, trigonometric, and Jacobi elliptic solutions. The main goal was to clarify how fractional derivatives, defined by the parameter $ \beta $, affect the characteristics and behavior of these soliton solutions. The key outcomes indicate that variations in the parameter $ \beta $ lead to substantial changes in soliton amplitude, shape, and propagation patterns. Graphical illustrations clearly depict these transformations, highlighting how fractional derivatives have a major impact on the properties of solitons. Crucially, for certain fractional orders, the localization and stability of solitons are enhanced, which is essential for accurate modeling of nonlocal and dispersive effects in optical fibers. This work not only enhances fundamental understanding of nonlinear wave phenomena within optical communication systems but also offers valuable insights into using fractional calculus for designing and optimizing advanced photonic devices.
Author Badra, Niveen
Soliman, Mahmoud
Ramadan, M. Elsaid
Ahmed, Hamdy M.
Alkhatib, Soliman
Samir, Islam
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CorporateAuthor Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi Arabia
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt
Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, Egypt
College of Engineering and Technology, American University in the Emirates (AUE), Dubai intel Academic City, P. O. Box 503000, Dubai, UAE
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StartPage 7489
SubjectTerms fractional derivatives
improved modified extended tanh-function method
nonlinear schrödinger equation
soliton solutions
Title Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality
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