Two - dimensional solitons in media with the stripe - shaped nonlinearity modulation

TL;DR

This paper investigates the existence and stability of two-dimensional solitons in media with stripe-shaped nonlinearities, revealing that the shape of the stripe critically influences soliton stability and types, with stable solutions found for rectangular profiles.

Contribution

It introduces a model for 2D solitons with stripe-shaped nonlinearities and analyzes stability conditions, highlighting the impact of stripe shape on soliton stability and types, including double stripes.

Findings

Rectangular stripe supports stable 2D solitons.

Gaussian-shaped stripe makes all solitons unstable.

Double stripe admits stable symmetric and asymmetric solitons.

Abstract

We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. In recent works, it was concluded that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result crucially depends on the transverse shape of the stripe: while the rectangular profile supports stable 2D solitons, its smooth Gaussian-shaped counterpart makes all the solitons unstable. The double stripe with the rectangular profile admit stable solitons of three distinct types: symmetric and asymmetric ones with a single peak, and double-peak symmetric solitons. The shape and stability of single-peak solitons of either type are accurately predicted by the VA. Collisions between stable solitons are briefly considered too, by means of direct simulations. Depending on the relative velocity we observe excitation, decay or catastrophic self focusing.