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Extraction of new solitary wave solutions in a generalized nonlinear Schrödinger equation comprising weak nonlocality

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  • Miguel Vivas-Cortez
  • Ghada Ali Basendwah
  • Beenish Rani
  • Nauman Raza
  • Mohammed Kbiri Alaoui

Abstract

This article delves into examining exact soliton solutions within the context of the generalized nonlinear Schrödinger equation. It covers higher-order dispersion with higher order nonlinearity and a parameter associated with weak nonlocality. To tackle this equation, two reputable methods are harnessed: the sine-Gordon expansion method and the G ′ / ( b G ′ + G + a )-expansion method. These methods are employed alongside suitable traveling wave transformation to yield novel, efficient single-wave soliton solutions for the governing model. To deepen our grasp of the equation’s physical significance, we utilize Wolfram Mathematica 12, a computational tool, to produce both 3D and 2D visual depictions. These graphical representations shed light on diverse facets of the equation’s dynamics, offering invaluable insights. Through the manipulation of parameter values, we achieve an array of solutions, encompassing kink-type, dark soliton, and solitary wave solutions. Our computational analysis affirms the effectiveness and versatility of our methods in tackling a wide spectrum of nonlinear challenges within the domains of mathematical science and engineering.

Suggested Citation

  • Miguel Vivas-Cortez & Ghada Ali Basendwah & Beenish Rani & Nauman Raza & Mohammed Kbiri Alaoui, 2024. "Extraction of new solitary wave solutions in a generalized nonlinear Schrödinger equation comprising weak nonlocality," PLOS ONE, Public Library of Science, vol. 19(5), pages 1-15, May.
    • Handle: RePEc:plo:pone00:0297898
    DOI: 10.1371/journal.pone.0297898
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Kudryashov, Nikolay A., 2020. "Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 371(C).
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