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Bubbles and W-shaped solitons in Kerr media with fractional diffraction

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Abstract

We demonstrate that, with the help of a Gaussian potential barrier, dark modes in the form of a local depression (“bubbles”) can be supported by the repulsive Kerr nonlinearity in combination with fractional dimension. Similarly, W-shaped modes are supported by a double potential barrier. Families of the modes are constructed in a numerical form, and also by means of the Thomas–Fermi and variational approximations. All these modes are stable, which is predicted by computation of eigenvalues for small perturbations and confirmed by direct numerical simulations.

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Funding

National Major Instruments and Equipment Development Project of National Natural Science Foundation of China (No. 61827815); National Natural Science Foundation of China (No. 62075138); Science and Technology Project of Shenzhen (JCYJ20190808121817100, JCYJ20190808164007485, JSGG20191231144201722); Israel Science Foundation (No. 1286/17).

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Authors and Affiliations

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

    Liangwei Zeng, Yi Cai, Xiaowei Lu, Qifan Zhu & Jingzhen Li

  2. Shenzhen Key Laboratory of Micro-Nano Photonic Information Technology, Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronics Engineering, Shenzhen University, Shenzhen, 518060, China

    Liangwei Zeng, Yi Cai, Xiaowei Lu, Qifan Zhu & Jingzhen Li

  3. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and the Center for Light-Matter Interaction, Tel Aviv University, P.O.B. 39040, Ramat Aviv, Tel Aviv, Israel

    Boris A. Malomed

  4. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile

    Boris A. Malomed

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

    Dumitru Mihalache

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  1. Liangwei Zeng
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  2. Boris A. Malomed
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  3. Dumitru Mihalache
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Zeng, L., Malomed, B.A., Mihalache, D. et al. Bubbles and W-shaped solitons in Kerr media with fractional diffraction. Nonlinear Dyn 104, 4253–4264 (2021). https://doi.org/10.1007/s11071-021-06459-3

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