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

TL;DR

This paper explores the creation and stability of multi-soliton configurations in a two-dimensional nonlinear medium with a triangular pattern of quadratic nonlinearity peaks, revealing stable symmetric and asymmetric states, bistability, and vortex structures.

Contribution

It introduces new multi-soliton sets with a triangular nonlinear modulation and analyzes their stability, including symmetric, asymmetric, and vortex configurations, which was not previously studied in this context.

Findings

Stable symmetric multi-solitons of 1, 4, or 7 units

Stable asymmetric multi-solitons of 1, 2, or 3 units

Existence of vortex rings composed of three solitons

Abstract

We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating 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.