Implicit Quiescent Optical Soliton Perturbation with Nonlinear Chromatic Dispersion and Kudryashov’s Self-Phase Modulation Structures for the Complex Ginzburg–Landau Equation Using Lie Symmetry: Linear Temporal Evolution

Abdullahi Rashid Adem; Oswaldo González-Gaxiola; Anjan Biswas

doi:10.3390/appliedmath5030119

Implicit Quiescent Optical Soliton Perturbation with Nonlinear Chromatic Dispersion and Kudryashov’s Self-Phase Modulation Structures for the Complex Ginzburg–Landau Equation Using Lie Symmetry: Linear Temporal Evolution

Abdullahi Rashid Adem, Oswaldo González-Gaxiola, Anjan Biswas^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

This paper investigates quiescent solitons in optical fibers and crystals, modeled by the complicated Ginzburg–Landau equation incorporating nonlinear chromatic dispersion and six self-phase modulation structures introduced by Kudryashov. The model is formulated with linear temporal evolution and analyzed using Lie symmetry methods. The study also identified parameter constraints under which solutions exist.

Original language	English
Article number	119
Journal	AppliedMath
Volume	5
Issue number	3
DOIs	https://doi.org/10.3390/appliedmath5030119
Publication status	Published - Sept 2025
Externally published	Yes

Keywords

Lie symmetry
chromatic dispersion
quiescent solitons
waveguides

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title = "Implicit Quiescent Optical Soliton Perturbation with Nonlinear Chromatic Dispersion and Kudryashov{\textquoteright}s Self-Phase Modulation Structures for the Complex Ginzburg–Landau Equation Using Lie Symmetry: Linear Temporal Evolution",

abstract = "This paper investigates quiescent solitons in optical fibers and crystals, modeled by the complicated Ginzburg–Landau equation incorporating nonlinear chromatic dispersion and six self-phase modulation structures introduced by Kudryashov. The model is formulated with linear temporal evolution and analyzed using Lie symmetry methods. The study also identified parameter constraints under which solutions exist.",

keywords = "Lie symmetry, chromatic dispersion, quiescent solitons, waveguides",

author = "\{Rashid Adem\}, Abdullahi and Oswaldo Gonz{\'a}lez-Gaxiola and Anjan Biswas",

note = "Publisher Copyright: {\textcopyright} 2025 by the authors.",

year = "2025",

month = sep,

doi = "10.3390/appliedmath5030119",

language = "English",

volume = "5",

journal = "AppliedMath",

issn = "2673-9909",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "3",

}

Implicit Quiescent Optical Soliton Perturbation with Nonlinear Chromatic Dispersion and Kudryashov’s Self-Phase Modulation Structures for the Complex Ginzburg–Landau Equation Using Lie Symmetry: Linear Temporal Evolution. / Rashid Adem, Abdullahi; González-Gaxiola, Oswaldo; Biswas, Anjan.
In: AppliedMath, Vol. 5, No. 3, 119, 09.2025.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Implicit Quiescent Optical Soliton Perturbation with Nonlinear Chromatic Dispersion and Kudryashov’s Self-Phase Modulation Structures for the Complex Ginzburg–Landau Equation Using Lie Symmetry

T2 - Linear Temporal Evolution

AU - Rashid Adem, Abdullahi

AU - González-Gaxiola, Oswaldo

AU - Biswas, Anjan

PY - 2025/9

Y1 - 2025/9

N2 - This paper investigates quiescent solitons in optical fibers and crystals, modeled by the complicated Ginzburg–Landau equation incorporating nonlinear chromatic dispersion and six self-phase modulation structures introduced by Kudryashov. The model is formulated with linear temporal evolution and analyzed using Lie symmetry methods. The study also identified parameter constraints under which solutions exist.

AB - This paper investigates quiescent solitons in optical fibers and crystals, modeled by the complicated Ginzburg–Landau equation incorporating nonlinear chromatic dispersion and six self-phase modulation structures introduced by Kudryashov. The model is formulated with linear temporal evolution and analyzed using Lie symmetry methods. The study also identified parameter constraints under which solutions exist.

KW - Lie symmetry

KW - chromatic dispersion

KW - quiescent solitons

KW - waveguides

UR - https://www.scopus.com/pages/publications/105017433632

U2 - 10.3390/appliedmath5030119

DO - 10.3390/appliedmath5030119

M3 - Article

AN - SCOPUS:105017433632

SN - 2673-9909

VL - 5

JO - AppliedMath

JF - AppliedMath

IS - 3

M1 - 119

ER -

Implicit Quiescent Optical Soliton Perturbation with Nonlinear Chromatic Dispersion and Kudryashov’s Self-Phase Modulation Structures for the Complex Ginzburg–Landau Equation Using Lie Symmetry: Linear Temporal Evolution

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Keywords

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