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M-derivative applied to the soliton solutions for the Lakshmanan–Porsezian–Daniel equation with dual-dispersion for optical fibers

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Abstract

Optical dispersive soliton solutions for the fractional Lakshmanan–Porsezian–Daniel equation for optical fibers are studied in this paper considering the M-derivative of order \(\chi\). The analytical method considered here is based on the Jacobi elliptic function (JEF) anzätz method. We found new optical soliton solutions that are relevant for the dynamics inside optical fibers. Some constraints conditions arise between the parameters of the JEF soliton solutions. Typical behaviour of the soliton solutions obtained is depicted in some interesting simulations.

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Acknowledgements

We gratefully acknowledge to the Universidad Autónoma de la Ciudad de México for supporting and facilitating this research work. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014. Huitzilín Yépez Martínez and José Francisco Gómez Aguilar acknowledges the support provided by SNI-CONACyT.

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Authors and Affiliations

  1. Universidad Autónoma de la Ciudad de México, Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, C.P. 09790, Mexico, D.F., Mexico

    H. Yépez-Martínez

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

    J. F. Gómez-Aguilar

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  1. H. Yépez-Martínez
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  2. J. F. Gómez-Aguilar
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Correspondence to J. F. Gómez-Aguilar.

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Yépez-Martínez, H., Gómez-Aguilar, J.F. M-derivative applied to the soliton solutions for the Lakshmanan–Porsezian–Daniel equation with dual-dispersion for optical fibers. Opt Quant Electron 51, 31 (2019). https://doi.org/10.1007/s11082-018-1740-5

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