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Localized solutions of inhomogeneous saturable nonlinear Schrödinger equation

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Abstract

In this paper, we obtain localized solutions of a nonhomogeneous saturable nonlinear system well described by a nonautonomous nonlinear Schrödinger equation. The nonlinearity under consideration disappears in the limiting case of zero saturation, causing the system to be modeled by a linear Schrödinger equation. We employ the similarity transformation technique to convert the nonautonomous equation into an autonomous one. The modulation patterns, generally applied by inhomogeneities of linear and nonlinear coefficients, need to satisfy a set of conditional equations obtained during the similarity transformation. Finally, we consider different modulation patterns that change the position of the center of mass and/or the width of the localized solutions and investigate their linear stability, in which we obtain some examples that can be stable, depending on the specific values of the system parameters.

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Acknowledgements

The authors acknowledge the financial support of the Brazilian agencies CNPq (No. 306065/2019-3, No. 425718/2018-2, No. 312723/2018-0, No. 407469/2021-4, and Sisphoton Laboratory-MCTI No. 440225/2021-3), CAPES, and FAPEG (PRONEM Grant No. 201710267000540, PRONEX Grant No. 201710267000503). This work was also performed as part of the Brazilian National Institute of Science and Technology (INCT) for Quantum Information (Grant No. 465469/2014-0).

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  1. Instituto de Física, Universidade Federal de Goiás, Goiânia, GO, 74690-900, Brazil

    Maurilho R. da Rocha, Ardiley T. Avelar & Wesley B. Cardoso

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  1. Maurilho R. da Rocha
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Rocha, M.R.d., Avelar, A.T. & Cardoso, W.B. Localized solutions of inhomogeneous saturable nonlinear Schrödinger equation. Nonlinear Dyn 111, 4769–4777 (2023). https://doi.org/10.1007/s11071-022-08104-z

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