Domain walls in fractional media

TL;DR

This paper predicts and analyzes stable domain wall states in fractional nonlinear media with two-component systems, exploring their existence, stability, and properties across various parameters including fractional diffraction and immiscibility thresholds.

Contribution

It introduces the first prediction and numerical validation of domain walls in fractional media, including analytical scaling and asymmetric solutions.

Findings

Stable domain walls exist for all Levy indices below 2.

Domain walls are stable across a range of XPM/SPM ratios.

Analytical scaling laws for domain wall width are derived.

Abstract

Currently, much interest is drawn to the analysis of optical and matter-wave modes supported by the fractional diffraction in nonlinear media. We predict a new type of such states, in the form of domain walls (DWs) in the two-component system of immiscible fields. Numerical study of the underlying system of fractional nonlinear Schroedinger equations demonstrates the existence and stability of DWs at all values of the respective Levy index (a < 2) which determines the fractional diffraction, and at all values of the XPM/SPM ratio b in the two-component system above the immiscibility threshold. The same conclusion is obtained for DWs in the system which includes the linear coupling, alongside the XPM interaction between the immiscible components. Analytical results are obtained for the scaling of the DW's width. The DW solutions are essentially simplified in the special case of b = 3, as well as close to the immiscibility threshold. In addition to symmetric DWs, asymmetric ones are constructed too, in the system with unequal diffraction coefficients and/or different Levy indices of the two components.