Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative

The generalized auxiliary equation approach is employed to derive enhanced solitary wave solutions for nonlinear directional couplers utilizing optical metamaterials. The study highlights the influence of the fractional Beta derivative parameter on soliton dynamics, demonstrating its crucial role in...

Full description

Saved in:
Bibliographic Details
Main Authors: Adil Jhangeer, Maham Munawar, Mudassar Imran, Atef Abdelkader
Format: Article
Language:English
Published: Elsevier 2025-06-01
Series:Partial Differential Equations in Applied Mathematics
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S266681812500124X
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849719881125068800
author Adil Jhangeer
Maham Munawar
Mudassar Imran
Atef Abdelkader
author_facet Adil Jhangeer
Maham Munawar
Mudassar Imran
Atef Abdelkader
author_sort Adil Jhangeer
collection DOAJ
description The generalized auxiliary equation approach is employed to derive enhanced solitary wave solutions for nonlinear directional couplers utilizing optical metamaterials. The study highlights the influence of the fractional Beta derivative parameter on soliton dynamics, demonstrating its crucial role in shaping soliton amplitudes and wave structures. Various soliton families including semi-bright solitons, solitary dark pitched solitons, single solitons, and mixed hyperbolic, trigonometric, and rational solitons are systematically constructed. Furthermore, the impact of overlapping functions on soliton interactions is investigated, revealing their significant role in amplitude modulation, wave localization, and phase shifts. This insight provides a deeper understanding of nonlinear optical interactions and enhances the accuracy of wave propagation models in directional couplers. These solutions are further analyzed using advanced computational tools to extract numerical insights. Beyond mathematical derivations, the physical relevance of these findings is explored through phase portrait analysis, quasi-periodic patterns, Lyapunov exponents, 2D Power spectrum and 3D attractors. These analyses provide a deeper understanding of energy transfer mechanisms, stability characteristics, and nonlinear optical interactions within directional couplers. The sensitivity evaluation underscores the system’s response to perturbations, offering valuable implications for the design and optimization of optical communication systems, signal processing, and photonic device engineering.
format Article
id doaj-art-3ad6d7e869c845b18202e861bfc15ea6
institution DOAJ
issn 2666-8181
language English
publishDate 2025-06-01
publisher Elsevier
record_format Article
series Partial Differential Equations in Applied Mathematics
spelling doaj-art-3ad6d7e869c845b18202e861bfc15ea62025-08-20T03:12:02ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410119710.1016/j.padiff.2025.101197Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivativeAdil Jhangeer0Maham Munawar1Mudassar Imran2Atef Abdelkader3IT4Innovations, VSB-Technical University of Ostrava, Ostrava-Poruba, Czech RepublicDepartment of Mathematics, University of Engineering and Technology, Pakistan; Corresponding author.College of Humanities and Sciences, Ajman University, Ajman, P.O. Box 346, United Arab EmiratesCollege of Humanities and Sciences, Ajman University, Ajman, P.O. Box 346, United Arab EmiratesThe generalized auxiliary equation approach is employed to derive enhanced solitary wave solutions for nonlinear directional couplers utilizing optical metamaterials. The study highlights the influence of the fractional Beta derivative parameter on soliton dynamics, demonstrating its crucial role in shaping soliton amplitudes and wave structures. Various soliton families including semi-bright solitons, solitary dark pitched solitons, single solitons, and mixed hyperbolic, trigonometric, and rational solitons are systematically constructed. Furthermore, the impact of overlapping functions on soliton interactions is investigated, revealing their significant role in amplitude modulation, wave localization, and phase shifts. This insight provides a deeper understanding of nonlinear optical interactions and enhances the accuracy of wave propagation models in directional couplers. These solutions are further analyzed using advanced computational tools to extract numerical insights. Beyond mathematical derivations, the physical relevance of these findings is explored through phase portrait analysis, quasi-periodic patterns, Lyapunov exponents, 2D Power spectrum and 3D attractors. These analyses provide a deeper understanding of energy transfer mechanisms, stability characteristics, and nonlinear optical interactions within directional couplers. The sensitivity evaluation underscores the system’s response to perturbations, offering valuable implications for the design and optimization of optical communication systems, signal processing, and photonic device engineering.http://www.sciencedirect.com/science/article/pii/S266681812500124XNonlinear directional couplersOptical metamaterialsOverlapping functionsChaotic behaviorsMultistabilityLyapunov exponent
spellingShingle Adil Jhangeer
Maham Munawar
Mudassar Imran
Atef Abdelkader
Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative
Partial Differential Equations in Applied Mathematics
Nonlinear directional couplers
Optical metamaterials
Overlapping functions
Chaotic behaviors
Multistability
Lyapunov exponent
title Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative
title_full Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative
title_fullStr Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative
title_full_unstemmed Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative
title_short Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative
title_sort chaotic demonstration of the twin core couplers with kerr law non linearity employing beta derivative
topic Nonlinear directional couplers
Optical metamaterials
Overlapping functions
Chaotic behaviors
Multistability
Lyapunov exponent
url http://www.sciencedirect.com/science/article/pii/S266681812500124X
work_keys_str_mv AT adiljhangeer chaoticdemonstrationofthetwincorecouplerswithkerrlawnonlinearityemployingbetaderivative
AT mahammunawar chaoticdemonstrationofthetwincorecouplerswithkerrlawnonlinearityemployingbetaderivative
AT mudassarimran chaoticdemonstrationofthetwincorecouplerswithkerrlawnonlinearityemployingbetaderivative
AT atefabdelkader chaoticdemonstrationofthetwincorecouplerswithkerrlawnonlinearityemployingbetaderivative