Stable and oscillating solitons of $\mathcal{PT}$-symmetric couplers with gain and loss in fractional dimension

TL;DR

This paper investigates stable and oscillating $ ext{PT}$-symmetric coupled solitons in fractional-dimensional models with gain and loss, highlighting the effects of cross-interactions modulation on stability and dynamics.

Contribution

It introduces new families of $ ext{PT}$-symmetric coupled solitons in fractional dimensions, analyzing their stability, oscillation behavior, and the impact of cross-interactions modulation.

Findings

Stability area is broader with cross-interactions modulation.

Oscillating solitons exist with controllable periods.

Models with CIM show enhanced stability and dynamic features.

Abstract

Families of coupled solitons of $\mathcal{PT}$-symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions modulation (CIM), are reported. Profiles, powers, stability areas, and propagation dynamics of the obtained $\mathcal{PT}$-symmetric coupled solitons are investigated. By comparing the results of the models with and without CIM, we find that the stability area of the model with CIM is much broader than the one without CIM. Remarkably, oscillating $\mathcal{PT}$-symmetric coupled solitons can also exist in the model of CIM with the same coefficients of the self- and cross-interactions modulations. In addition, the period of these oscillating coupled solitons can be controlled by the linear coupling coefficient.