Eur. Phys. J. Special Topics 227, 533–549 (2018)
https://doi.org/10.1140/epjst/e2018-00127-4

Regular Article

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

¹ Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
² ITMO University, St. Petersburg 197101, Russia

^a e-mail: malomed@eng.tau.ac.il

Received: 29 November 2017
Published online: 4 October 2018

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.