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...
Saved in:
| Main Authors: | , , , |
|---|---|
| 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 |