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Modulational instability, optical solitons and travelling wave solutions to two nonlinear models in birefringent fibres with and without four-wave mixing terms

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Abstract

The paper aims to construct optical solitons and travelling wave solutions to two birefringent nonlinear models which consist of two-component form of vector solitons in optical fibre: the Biswas–Arshed model with Kerr-type nonlinearity and without four-wave mixing terms and the nonlinear Schrödinger equation with quadratic-cubic law of refractive index along with four-wave mixing terms. These nonlinear Schrödinger equations are applied in many physical and engineering fields. Optical solitons are considered in the context of photonic crystal fibres, couplers, polarisation-preserving fibres, metamaterials, birefringent fibres, and so on. Two reliable integration architectures, namely, the extended simplest equation method and the generalised sub-ODE approach, are adopted. As a result, bright soliton, kink and dark soliton, singular soliton, hyperbolic wave, a periodic wave, elliptic function solutions of Weierstrass and Jacobian types, and other travelling wave solutions, such as breather solutions and optical rogons, are derived, together with the existence conditions. In addition, the amplitude and intensity diagrams are portrayed by taking appropriate values for a few selected solutions. Furthermore, based on linear stability analysis, the modulation instability was explored for the obtained steady-state solutions. The reported results of this paper can enrich the dynamical behaviours of the two considered nonlinear models and can be useful in many scientific fields, such as mathematical physics, mathematical biology, telecommunications, engineering and optical fibres. This study confirms that the proposed approaches are sufficiently effective in extracting a variety of analytical solutions to other nonlinear models in both engineering and science.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Bahira, 22514, Egypt

    Shoukry El-Ganaini

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Wen-Xiu Ma

  3. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Wen-Xiu Ma

  4. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Wen-Xiu Ma

  5. Department of Mathematics and Statistical Sciences, North-West University, Mafikeng Campus, Mmabatho, 2735, South Africa

    Wen-Xiu Ma

  6. Department of Physics, Government College for Women, Bastara (Gharaunda), Karnal, 132 114, India

    Hitender Kumar

Authors
  1. Shoukry El-Ganaini
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  2. Wen-Xiu Ma
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  3. Hitender Kumar
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Correspondence to Hitender Kumar.

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El-Ganaini, S., Ma, WX. & Kumar, H. Modulational instability, optical solitons and travelling wave solutions to two nonlinear models in birefringent fibres with and without four-wave mixing terms. Pramana - J Phys 97, 119 (2023). https://doi.org/10.1007/s12043-023-02572-7

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  • DOI: https://doi.org/10.1007/s12043-023-02572-7

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