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Novel optical solitons to the perturbed Gerdjikov–Ivanov equation via collective variables

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Abstract

The objective of this manuscript is to study the collective variable (CV) technique to explore an important form of Schrödinger equation known as the Gerdjikov–Ivanov (GI) equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters. These parameters are temporal position, amplitude, width, chirp, phase, and frequency known as CVs. This is an effective and dynamic mathematical gadget to obtain soliton solutions of non-dimensional as well as perturbed GI equations. Moreover, an established numerical scheme that is the fourth-order Runge–Kutta method is exerted for the numerical simulation of the revealing coupled system of six ordinary differential equations which represent all the CVs included in the pulse ansatz. The CV approach is used to determine the evolution of pulse parameters with the propagation distance and illustrated them graphically. Furthermore, figures show the compelling periodic oscillations of pulse chirp, width, frequency and amplitude of soliton. For various values of super-Gaussian pulse parameters, the numerical behavior of solitons to illustrate variations in CVs is provided. Other significant aspects with regards to the current investigation are also inferred.

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Acknowledgements

José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Lahore, 54590, Pakistan

    Zara Hassan & Nauman Raza

  2. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

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  1. Zara Hassan
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  2. Nauman Raza
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  3. J. F. Gómez-Aguilar
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Contributions

ZH: Conceptualization, methodology, writing original draft preparation; NR: methodology, data curation, writing-original draft preparation; JFG: conceptualization, methodology, writing—original draft preparation, software, supervision.

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Correspondence to J. F. Gómez-Aguilar.

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Hassan, Z., Raza, N. & Gómez-Aguilar, J.F. Novel optical solitons to the perturbed Gerdjikov–Ivanov equation via collective variables. Opt Quant Electron 53, 474 (2021). https://doi.org/10.1007/s11082-021-03123-3

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