Implicit Quiescent Solitons in Optical Metamaterials with Nonlinear Chromatic Dispersion and an Array of Self-Phase Modulation Structures with Generalized Temporal Evolution by Lie Symmetry

Abdullahi Rashid Adem; Oswaldo González-Gaxiola; Ahmed H. Arnous; Lina S. Calucag; Anjan Biswas

doi:10.3390/telecom7010006

Implicit Quiescent Solitons in Optical Metamaterials with Nonlinear Chromatic Dispersion and an Array of Self-Phase Modulation Structures with Generalized Temporal Evolution by Lie Symmetry

Abdullahi Rashid Adem
, Oswaldo González-Gaxiola
, Ahmed H. Arnous
, Lina S. Calucag
, Anjan Biswas^*

^*Corresponding author for this work

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

Abstract

The current paper retrieves implicit quiescent soliton solutions to optical metamaterials with nonlinear chromatic dispersion with generalized temporal evolution. Seven forms of self-phase modulation structures, as proposed by Kudryashov with time, are taken up. The implemented integration algorithm is Lie symmetry. A few of the solutions are in quadratures, while others are in terms of special functions. We also characterize the parameters that constrain the existence of such solutions.

Original language	English
Article number	6
Journal	Telecom
Volume	7
Issue number	1
DOIs	https://doi.org/10.3390/telecom7010006
Publication status	Published - Feb 2026
Externally published	Yes

Keywords

chromatic dispersion
nonlinear Schrödinger equation
self-phase modulation
solitons

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10.3390/telecom7010006

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title = "Implicit Quiescent Solitons in Optical Metamaterials with Nonlinear Chromatic Dispersion and an Array of Self-Phase Modulation Structures with Generalized Temporal Evolution by Lie Symmetry",

abstract = "The current paper retrieves implicit quiescent soliton solutions to optical metamaterials with nonlinear chromatic dispersion with generalized temporal evolution. Seven forms of self-phase modulation structures, as proposed by Kudryashov with time, are taken up. The implemented integration algorithm is Lie symmetry. A few of the solutions are in quadratures, while others are in terms of special functions. We also characterize the parameters that constrain the existence of such solutions.",

keywords = "chromatic dispersion, nonlinear Schr{\"o}dinger equation, self-phase modulation, solitons",

author = "Adem, \{Abdullahi Rashid\} and Oswaldo Gonz{\'a}lez-Gaxiola and Arnous, \{Ahmed H.\} and Calucag, \{Lina S.\} and Anjan Biswas",

note = "Publisher Copyright: {\textcopyright} 2026 by the authors.",

year = "2026",

month = feb,

doi = "10.3390/telecom7010006",

language = "English",

volume = "7",

journal = "Telecom",

issn = "2673-4001",

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

number = "1",

}

Implicit Quiescent Solitons in Optical Metamaterials with Nonlinear Chromatic Dispersion and an Array of Self-Phase Modulation Structures with Generalized Temporal Evolution by Lie Symmetry. / Adem, Abdullahi Rashid; González-Gaxiola, Oswaldo; Arnous, Ahmed H. et al.
In: Telecom, Vol. 7, No. 1, 6, 02.2026.

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

TY - JOUR

T1 - Implicit Quiescent Solitons in Optical Metamaterials with Nonlinear Chromatic Dispersion and an Array of Self-Phase Modulation Structures with Generalized Temporal Evolution by Lie Symmetry

AU - Adem, Abdullahi Rashid

AU - González-Gaxiola, Oswaldo

AU - Arnous, Ahmed H.

AU - Calucag, Lina S.

AU - Biswas, Anjan

PY - 2026/2

Y1 - 2026/2

N2 - The current paper retrieves implicit quiescent soliton solutions to optical metamaterials with nonlinear chromatic dispersion with generalized temporal evolution. Seven forms of self-phase modulation structures, as proposed by Kudryashov with time, are taken up. The implemented integration algorithm is Lie symmetry. A few of the solutions are in quadratures, while others are in terms of special functions. We also characterize the parameters that constrain the existence of such solutions.

AB - The current paper retrieves implicit quiescent soliton solutions to optical metamaterials with nonlinear chromatic dispersion with generalized temporal evolution. Seven forms of self-phase modulation structures, as proposed by Kudryashov with time, are taken up. The implemented integration algorithm is Lie symmetry. A few of the solutions are in quadratures, while others are in terms of special functions. We also characterize the parameters that constrain the existence of such solutions.

KW - chromatic dispersion

KW - nonlinear Schrödinger equation

KW - self-phase modulation

KW - solitons

UR - https://www.scopus.com/pages/publications/105031369510

U2 - 10.3390/telecom7010006

DO - 10.3390/telecom7010006

M3 - Article

AN - SCOPUS:105031369510

SN - 2673-4001

VL - 7

JO - Telecom

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M1 - 6

ER -

Implicit Quiescent Solitons in Optical Metamaterials with Nonlinear Chromatic Dispersion and an Array of Self-Phase Modulation Structures with Generalized Temporal Evolution by Lie Symmetry

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Keywords

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