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Influence of fourth-order dispersion on the Anderson localization

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Abstract

Anderson localization, which consists in the absence of wave dispersion due to disorder, brought to the field of optics and matter waves has greatly improved our understanding of fundamental processes, such as transport and multiple dispersion of light. In this paper, we investigate the existence of Anderson localization in the interplay of a standard group velocity dispersion and a fourth-order dispersion term in the nonlinear Schrödinger (NLS) equation in the presence of a quasiperiodic linear coefficient. We employ a variational approach with a Gaussian ansatz to describe the center of the localized state, while the tails are studied by direct numerical simulations of the NLS equation. These two approaches are important to distinguish the region of the solution presenting exponential decay, which is the main signature of the Anderson localization. The existence of Anderson localization has been confirmed by numerical simulations even when the system presents a small defocusing nonlinearity. In this sense, we reported how the fourth-order dispersion effect changes the existence region of the localized state by changing the critical values for the transition between the localized and delocalized states.

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Acknowledgements

The author acknowledges the financial support of the Brazilian agencies CNPq (\(\#\)304073/2016-4, \(\#\)306065/2019-3 & \(\#\)425718/2018-2), CAPES, and FAPEG (PRONEM \(\#\)201710267000540, PRONEX \(\#\)201710267000503). This work was also performed as part of the Brazilian National Institute of Science and Technology (INCT) for Quantum Information (\(\#\)465469/2014-0).

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  1. Instituto de Física, Universidade Federal de Goiás, Goiânia, Goiás, 74.690-900, Brazil

    Mateus C. P. dos Santos & Wesley B. Cardoso

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dos Santos, M.C.P., Cardoso, W.B. Influence of fourth-order dispersion on the Anderson localization. Nonlinear Dyn 101, 611–618 (2020). https://doi.org/10.1007/s11071-020-05788-z

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