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Effects of chaotic perturbations on a nonlinear system undergoing two-soliton collisions

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Abstract

In this work, we present a numerical study of two-soliton collisions in a system described by a cubic (Kerr-type) nonlinear Schrödinger equation whose nonlinearity has small chaotic imperfections. We use a logistic map in order to obtain a chaotic perturbation, where by defining the values of its seed and the interaction parameter, one can observe a disorder in the nonlinearity of the system. This disorder was varied by changing the parameter values and controlled via the Lyapunov exponent, however, always maintaining a fixed amplitude. We verified a direct relationship between the value of the Lyapunov coefficient and the formation of two-soliton bonded/unbonded states.

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Data Availability Statement

All data generated or analyzed during this study are included in this published article.

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Acknowledgements

We acknowledge financial support from the Brazilian agencies CNPq (#312723/2018-0, #425718/2018-2, #306065/2019-3, #404913/2018-0 & #303469/2019-6), CAPES and FAPEG (PRONEM #201710267000540, PRONEX #201710267000503), and Paraiba State Research Foundation, PRONEX #0015/2019. This work was performed as part of the Brazilian National Institute of Science and Technology for Quantum Information (INCT-IQ #465469/2014-0).

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Authors and Affiliations

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

    W. B. Cardoso & A. T. Avelar

  2. Departamento de Física, Universidade Federal da Paraíba, 58.051-970, João Pessoa, PB, Brazil

    D. Bazeia

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  1. W. B. Cardoso
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Cardoso, W.B., Avelar, A.T. & Bazeia, D. Effects of chaotic perturbations on a nonlinear system undergoing two-soliton collisions. Nonlinear Dyn 106, 3469–3477 (2021). https://doi.org/10.1007/s11071-021-06962-7

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