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Article

Highly Dispersive Optical Soliton Perturbation for Complex Ginzburg–Landau Equation, Implementing Three Forms of Self-Phase Modulation Structures with Power Law via Semi-Inverse Variation

by
Anjan Biswas
1,2,3,4,*,
Russell W. Kohl
5,
Milisha Hart-Simmons
1 and
Oswaldo González-Gaxiola
6
1
Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245-2715, USA
2
Department of Physics and Electronics, Khazar University, Baku AZ 1096, Azerbaijan
3
Department of Applied Sciences, Cross–Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania
4
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, South Africa
5
Department of Mathematics and Computer Science, University of Maryland Eastern Shore, Princess Anne, MD 21853, USA
6
Applied Mathematics and Systems Department, Universidad Autonoma Metropolitana–Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, Mexico
*
Author to whom correspondence should be addressed.
Telecom 2025, 6(3), 68; https://doi.org/10.3390/telecom6030068
Submission received: 23 July 2025 / Revised: 4 September 2025 / Accepted: 10 September 2025 / Published: 12 September 2025
(This article belongs to the Special Issue Optical Communication and Networking)
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Abstract

This paper provides highly dispersive optical soliton solutions to the perturbed complex Ginzburg–Landau equation. The self-phase modulation structures are maintained in three forms, which are derived from the power law of nonlinearity with arbitrary intensity. The paper employs the semi-inverse variational principle as its integration scheme, as conventional methods are incapable for it. The amplitude–width relation of the solitons is reconstructed by employing Cardano’s method to solve a cubic polynomial equation. Also presented are the necessary parameter constraints that naturally arise from the scheme. These findings enhance our understanding of soliton dynamics and pave the way for further research into more complex nonlinear systems. Future studies may explore the implications of these results in various physical contexts, potentially leading to novel applications in fields such as fiber optics and quantum fluid dynamics.
Keywords: Kudryashov model; Ginzburg–Landau equation; solitons; semi-inverse; Cardano; perturbation Kudryashov model; Ginzburg–Landau equation; solitons; semi-inverse; Cardano; perturbation

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MDPI and ACS Style

Biswas, A.; Kohl, R.W.; Hart-Simmons, M.; González-Gaxiola, O. Highly Dispersive Optical Soliton Perturbation for Complex Ginzburg–Landau Equation, Implementing Three Forms of Self-Phase Modulation Structures with Power Law via Semi-Inverse Variation. Telecom 2025, 6, 68. https://doi.org/10.3390/telecom6030068

AMA Style

Biswas A, Kohl RW, Hart-Simmons M, González-Gaxiola O. Highly Dispersive Optical Soliton Perturbation for Complex Ginzburg–Landau Equation, Implementing Three Forms of Self-Phase Modulation Structures with Power Law via Semi-Inverse Variation. Telecom. 2025; 6(3):68. https://doi.org/10.3390/telecom6030068

Chicago/Turabian Style

Biswas, Anjan, Russell W. Kohl, Milisha Hart-Simmons, and Oswaldo González-Gaxiola. 2025. "Highly Dispersive Optical Soliton Perturbation for Complex Ginzburg–Landau Equation, Implementing Three Forms of Self-Phase Modulation Structures with Power Law via Semi-Inverse Variation" Telecom 6, no. 3: 68. https://doi.org/10.3390/telecom6030068

APA Style

Biswas, A., Kohl, R. W., Hart-Simmons, M., & González-Gaxiola, O. (2025). Highly Dispersive Optical Soliton Perturbation for Complex Ginzburg–Landau Equation, Implementing Three Forms of Self-Phase Modulation Structures with Power Law via Semi-Inverse Variation. Telecom, 6(3), 68. https://doi.org/10.3390/telecom6030068

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