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Ultrashort self-similar periodic waves and similaritons in an inhomogeneous optical medium with an external source and modulated coefficients

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Abstract

In this paper, we use the similarity transformation to reduce the generalized higher-order nonlinear Schrödinger equation with space- and time-modulated coefficients incorporating group velocity dispersion, self-phase modulation, self-steepening, self-frequency shift, gain or loss term, differential gain or loss term, group velocity of the modes, and inhomogeneous source to Hirota equation with a varying source. Afterward, we reduce this Hirota equation to a second-order nonhomogeneous nonlinear ordinary differential equation with constant source via a plane wave transformation and some constraint conditions. Finally, by using Möbius transformation, various types of exact self-similar femtosecond solutions are deduced such as the bright and dark-type solitons with W-shaped profiles, the bell-shaped bright solitons, and the periodic wave solutions. The evolutional dynamics of these self-similar structures are investigated in periodic distributed system. Our analysis shows that a suitable choice of the amplitude of the source term, the gain or loss parameter, and the differential gain or loss parameter allows us to control the similariton structures. In addition, the stability analysis of the solutions is discussed numerically. Our results may be useful to explain some nonlinear wave phenomena in nonlinear optics and related fields.

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Acknowledgements

The authors would like to thank the referees for their valuables suggestions.

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Authors and Affiliations

  1. Higher Teachers’ Training College, University of Maroua, P.O. Box 55, Maroua, Cameroon

    Calvin Djoptoussia &  Alim

  2. Faculty of Sciences, University of Maroua, P.O. Box 814, Maroua, Cameroon

    Camus Gaston Latchio Tiofack

  3. National Advanced School of Engineering, University of Maroua, P.O. Box 46, Maroua, Cameroon

    Alidou Mohamadou

  4. Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana

    Timoléon Crépin Kofané

  5. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    Timoléon Crépin Kofané

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  1. Calvin Djoptoussia
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Djoptoussia, C., Tiofack, C.G.L., Alim et al. Ultrashort self-similar periodic waves and similaritons in an inhomogeneous optical medium with an external source and modulated coefficients. Nonlinear Dyn 107, 3833–3846 (2022). https://doi.org/10.1007/s11071-021-07173-w

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