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Multi-soliton states under triangular spatial modulation of the quadratic nonlinearity

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Abstract

We introduce multi-soliton sets in the two-dimensional medium with the χ(2) nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are constructed, and their stability is investigated. Stable symmetric patterns may be built of 1, 4, or 7 individual solitons, while stable asymmetric ones contain 1, 2, or 3 solitons. Symmetric and asymmetric patterns may demonstrate mutual bistability. The shift of the asymmetric single-soliton state from the central position is accurately predicted analytically. Vortex rings composed of three solitons are produced too.

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Authors and Affiliations

  1. Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    Vitaly Lutsky & Boris A. Malomed

  2. ITMO University, St. Petersburg, 197101, Russia

    Boris A. Malomed

Authors
  1. Vitaly Lutsky
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  2. Boris A. Malomed
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Correspondence to Boris A. Malomed.

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Lutsky, V., Malomed, B.A. Multi-soliton states under triangular spatial modulation of the quadratic nonlinearity. Eur. Phys. J. Spec. Top. 227, 533–549 (2018). https://doi.org/10.1140/epjst/e2018-00127-4

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  • DOI: https://doi.org/10.1140/epjst/e2018-00127-4

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