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Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a generalized Schrödinger equation

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Abstract

The main goal of the present study is to conduct a deeper investigation into a generalized Schrödinger equation describing the propagation of optical pulses in media. To this end, the dynamical system of the governing equation is derived using the Galilean transformation, and its bifurcation is carried out using the theory of the planar dynamical system. By considering a perturbed term in the resulting dynamical system, the existence of chaotic behaviors of the generalized Schrödinger equation is investigated by giving some two- and three-dimensional phase portraits. Additionally, the sensitivity analysis of the dynamical system is accomplished using the Runge–Kutta method validating that small changes in initial conditions do not affect the stability of the solution very much. In the end, several bright and dark solitons to the governing model are constructed using the method of the planar dynamical system. The results of the current paper show that bright and dark solitons can be effectively controlled in terms of their width and height.

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Authors and Affiliations

  1. Department of Mathematics, Near East University TRNC, Mersin 10, Turkey

    Kamyar Hosseini & Evren Hinçal

  2. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

    Mousa Ilie

Authors
  1. Kamyar Hosseini
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  2. Evren Hinçal
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  3. Mousa Ilie
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Correspondence to Kamyar Hosseini.

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Hosseini, K., Hinçal, E. & Ilie, M. Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a generalized Schrödinger equation. Nonlinear Dyn 111, 17455–17462 (2023). https://doi.org/10.1007/s11071-023-08759-2

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