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Solitons collision and multi-peak solutions for a new \((3+1)\)-dimensional NLSE describing pulse propagation in optical fibers

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Abstract

This template recoups one-soliton transformation, two and N-solitons interactions through Hirota bilinear method (HBM) for a new \((3+1)\)-dimensional nonlinear Schrödinger equation (NLSE) in optical fibers. The contribution of this paper is to apply the Hirota’s derivatives, generate bilinear equations and use ansatz functions approach (AFA) for the governing model. In addition to this, we compute M-shape rational solitons and their interaction with kink waves, homoclinic breathers, kink cross rational solitons and periodic cross rational solitons for governing model by utilizing the symbolic computation with logarithmic transformation and AFA. Furthermore, the multi-wave solitons and interactional phenomena are found by applying three waves approach. We construct 3D profiles for our solutions by choosing appropriate values.

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Authors and Affiliations

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

    Aly R. Seadawy

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

    Syed T. R. Rizvi & Sarfaraz Ahmed

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  1. Aly R. Seadawy
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  2. Syed T. R. Rizvi
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  3. Sarfaraz Ahmed
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S.A. and S.R. and A.S. wrote the main manuscript text and S.A. prepared figures 1-3. All authors reviewed the manuscript.

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Correspondence to Aly R. Seadawy.

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Seadawy, A.R., Rizvi, S.T.R. & Ahmed, S. Solitons collision and multi-peak solutions for a new \((3+1)\)-dimensional NLSE describing pulse propagation in optical fibers. Opt Quant Electron 55, 467 (2023). https://doi.org/10.1007/s11082-023-04743-7

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