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Explicit exact solutions and conservation laws in a medium with competing weakly nonlocal nonlinearity and parabolic law nonlinearity

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Abstract

In this paper, we studied a nonlinear wave equation that models the propagation of optical solutions in a weakly nonlocal and parabolic competing nonlinear medium. The exact traveling wave type solutions formulated in hyperbolic functions, rational and trigonometric functions multiplied by some exponential functions to the governing equation are determined explicitly by the extended form of the Kudryashov method. We have examined the behavior of the modulation instability (MI) growth rate. To substantiate the stability of the obtained dark and bell-shaped solitons, we use the split-step Fourier method. In addition, the conservation laws describing significant physical concepts of this equation are examined. Compared to the obtained results with Younis et al. (J Nonlinear Opt Phys Mater 24(04):1550049, 2015), Zhou et al. (Optik 124(22):5683–5686, 2013; Proc Rom Acad Ser A 16(2):152–159, 2015) and Akinyemi et al. (Optik 230:166281, 2021), we have shown the propagation of the solitonic waves which sometime tilt from right to left with stable shape.

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Authors and Affiliations

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

    Abbagari Souleymanou

  2. Laboratory of Mechanics, Materials and Structures, Department of physics, Faculty of Science, The University of Yaoundé I, P.O Box 812, Yaoundé, Cameroon

    Abbagari Souleymanou & Serge P. T. Mukam

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

    Alphonse Houwe

  4. Department of Physics, Faculty of Science, The University of Maroua, P.O Box 814, Maroua, Cameroon

    Alphonse Houwe

  5. School of Mathematics, University of the Witwatersrand, Johannesburg, Wits, 2050, South Africa

    A. H. Kara

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

    Hadi Rezazadeh

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

    Lanre Akinyemi

  8. Department of Physics, Faculty of Science, The University of Ngaoundéré, P.O Box 454, Ngaoundéré, Cameroon

    Serge Y. Doka

  9. National Advanced School of Engineering, The University of Yaoundé I, Yaoundé, Cameroon

    Thomas B. Bouetou

Authors
  1. Abbagari Souleymanou
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  2. Alphonse Houwe
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  3. A. H. Kara
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  4. Hadi Rezazadeh
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  5. Lanre Akinyemi
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  6. Serge P. T. Mukam
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  7. Serge Y. Doka
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  8. Thomas B. Bouetou
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Contributions

Souleymanou Abbagari: Conceptualization, Formal analysis, Investigation, Methodology, Writing-original draft, Resources, Software. Alphonse Houwe: Conceptualization, Investigation, Methodology, Writing-original draft, Resources, Software. A. H. Kara: Writing-original draft, Resources, Software. Hadi Rezazadeh: Writing-original draft, Resources, Software. Lanre Akinyemi: Writing-review and editing, Validation, Methodology, Resources, Software. Serge P T Mukamc: Review and editing, Formal analysis. Serge Y. Doka: Writing-review and editing, Formal analysis, Resources, Supervision. Thomas B. Bouetou: Writing-review and editing, Formal analysis, Resources, Supervision

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Correspondence to Abbagari Souleymanou, Alphonse Houwe or Lanre Akinyemi.

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Souleymanou, A., Houwe, A., Kara, A.H. et al. Explicit exact solutions and conservation laws in a medium with competing weakly nonlocal nonlinearity and parabolic law nonlinearity. Opt Quant Electron 55, 464 (2023). https://doi.org/10.1007/s11082-023-04694-z

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