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Peculiar optical solitons and modulated waves patterns in anti-cubic nonlinear media with cubic–quintic nonlinearity

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Abstract

In this work, we investigate diverse analytical solutions and modulation instability of the nonlinear Schrödinger equation with an anti-cubic nonlinear term. We use the traveling wave transformation and the New Generalized Extended Direct Algebraic Method to perform a variety of exact traveling wave soliton-like solutions. The obtained solutions are among other trigonometric function solutions, complex soliton solutions, and rational solutions. A particular behavior has been depicted in self-focusing and defocusing nonlinearity where dark soliton changes to super rogue waves and breather soliton is obtained. We then use the linearizing scheme to get the growth rate of modulation instability. For a specific value of the excitation wave number and a specific time of simulation, diverse waveforms of the modulated waves are obtained. We have demonstrated that the combined dispersion and nonlinear terms, as well as the anti-cubic nonlinear term, can develop modulation instability. To confirm the predictions based on the analytical results, we use the direct numerical simulation, from which we have displayed a modulation wave of the growth rate modulation instability. It results equally that the anti-cubic nonlinearity is an important object to control the propagation of the solitonic waves in the nonlinear systems.

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Authors and Affiliations

  1. Department of Marine Engineering, Limbé Nautical Arts and Fisheries Institute, P.O. Box 485, Limbe, Cameroon

    Alphonse Houwe

  2. Department of Basic Science, National Advanced School of Mines and Petroleum Industries, The University of Maroua, P.O Box 08, Kaele, Cameroon

    Souleymanou Abbagari

  3. Department of Mathematics, Lafayette College, Easton, PA, USA

    Lanre Akinyemi

  4. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

  5. Department of Physics, Faculty of Science, The University of Ngaoundèré, P.O. Box 454, Ngaoundèré, Cameroon

    Serge Y. Doka

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  1. Alphonse Houwe
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  2. Souleymanou Abbagari
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  3. Lanre Akinyemi
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  4. Hadi Rezazadeh
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  5. Serge Y. Doka
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Houwe, A., Abbagari, S., Akinyemi, L. et al. Peculiar optical solitons and modulated waves patterns in anti-cubic nonlinear media with cubic–quintic nonlinearity. Opt Quant Electron 55, 719 (2023). https://doi.org/10.1007/s11082-023-04950-2

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