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Envelope solitons, multi-peak solitons and breathers in optical fibers via Chupin Liu’s theorem and polynomial law of nonlinearity

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Abstract

This paper studies the \((1 + 1)\)-dimensional nonlinear Schrödinger equation via polynomial law of nonlinearity which arises in nonlinear optical fibers and Bragg gratings. The envelope solitons as a entire are separated into two types: dark and bright solitons, which exist in the anomalous and normal dispersion regions, respectively. Grey and black optical solitons of the stated model are reported through appropriate complex envelope ansatz solution. With the usage of Chupin Liu’s theorem to the grey and black solitons, we evaluate new categories of combined optical soliton solutions. In addition, propagation behaviours for homoclinic breathers, multiwaves and M-shaped rational solitons are analytically examined via logarithmic transformation with ansatz functions approach. Multiwave solitons are reported by using three-waves technique. Furthermore two kinds of interactions for M-shape soliton through exponential functions are examined.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan

    Sarfaraz Ahmed & Syed T. R. Rizvi

  2. Mathematics Department, Faculty of Science, Taibah University, 41411, Al-Madinah Al-Munawarah, Kingdom of Saudi Arabia

    Aly R. Seadawy

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  1. Sarfaraz Ahmed
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Correspondence to Aly R. Seadawy.

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Ahmed, S., Seadawy, A.R. & Rizvi, S.T.R. Envelope solitons, multi-peak solitons and breathers in optical fibers via Chupin Liu’s theorem and polynomial law of nonlinearity. Opt Quant Electron 55, 632 (2023). https://doi.org/10.1007/s11082-023-04902-w

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