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Multiple-peak and multiple-ring solitons in the nonlinear Schrödinger equation with inhomogeneous self-defocusing nonlinearity

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Abstract

We prove that inhomogeneous defocusing cubic (Kerr) nonlinear media described by the nonlinear Schrödinger equation, which could be realized in the experiments of Bose–Einstein condensates or nonlinear optics, can support various types of one-dimensional (1D) multiple-peak and two-dimensional (2D) multiple-ring solitons, both with equal intensity peaks. The profiles of such equal-peak structures are determined by the parameters describing nonlinearity, and their relationship is clearly presented. Interestingly, the number of 1D equal peaks can be any positive odd natural number, and one of the 2D equal-annular-peak rings can be arbitrary positive integer, as long as the parameters of nonlinearity are set appropriately. It should be mentioned that the expressions on how to calculate the number of equal peaks are found phenomenologically but are clearly displayed. Besides fundamental modes, such nonlinear media can also support 2D vortical modes whose stability and instability domains appear alternately and are verified by the linear stability analysis and direct numerical simulations, which is in contrast to their fundamental nonvortical counterparts that are completely stable.

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

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Funding

Funding was provided by National Natural Science Foundation of China (62205224, 11774068); Guangdong Province Education Department Foundation of China (2018KZDXM044); Qatar National Research Fund (NPRP 12S-0205-190047); and Meizhou City Social Development Science and Technology Plan Project (2021B127).

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Authors and Affiliations

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

    Liangwei Zeng & Xing Zhu

  2. School of Optoelectronic Engineering, Guangdong Polytechnic Normal University, Guangzhou, 510665, China

    Xing Zhu

  3. Texas A &M University at Qatar, 23874, Doha, Qatar

    Milivoj R. Belić

  4. Horia Hulubei National Institute of Physics and Nuclear Engineering, 077125, Magurele, Bucharest, Romania

    Dumitru Mihalache

  5. 54th Research Institute of CETC, Shijiazhuang, 050011, China

    Jincheng Shi

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

    Junbo Chen

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  1. Liangwei Zeng
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Zeng, L., Zhu, X., Belić, M.R. et al. Multiple-peak and multiple-ring solitons in the nonlinear Schrödinger equation with inhomogeneous self-defocusing nonlinearity. Nonlinear Dyn 111, 5671–5680 (2023). https://doi.org/10.1007/s11071-022-08110-1

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