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Two-dimensional localized modes in saturable quintic nonlinear lattices

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Abstract

Stabilization of multidimensional solitons in self-focusing systems against the critical and supercritical collapse is a fundamental problem of nonlinear-wave dynamics in diverse physical media. One of solutions relies on the use of nonlinear lattices (NLs), i.e., spatially periodic modulation of the local strength of the nonlinearity. We demonstrate that NLs, which are built as square arrays of cylinders carrying the saturable quintic self-focusing nonlinearity, maintain the stability of several kinds of two-dimensional localized modes, including fundamental solitons, dipoles, triple-peak complexes, and off-site-centered vortices. This nonlinearity is a realistic model for the light propagation in the CS\(_{2}\) liquid, which is a medium used in many optical experiments. The stability of the modes is studied by means of the computation of eigenvalues for small perturbations and direct simulations of the perturbed evolution. The stability of all the localized modes complies with the Vakhitov–Kolokolov criterion.

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Data availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

National Natural Science Foundation of China (622 05224); Meizhou City Social Development Science and Technology Plan Project (2021B127).

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Authors and Affiliations

  1. 54th Research Institute of CETC, Shijiazhuang, 050011, China

    Jincheng Shi

  2. Department of Basic Courses, Guangzhou Maritime University, Guangzhou, 510725, China

    Liangwei Zeng

  3. College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China

    Liangwei Zeng

  4. School of Physics and Electronic Engineering, Jiaying University, Meizhou, 514015, China

    Junbo Chen

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Shi, J., Zeng, L. & Chen, J. Two-dimensional localized modes in saturable quintic nonlinear lattices. Nonlinear Dyn 111, 13415–13424 (2023). https://doi.org/10.1007/s11071-023-08558-9

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