Quiescent and traveling solitons in the fractional parametrically driven damped nonlinear Schrödinger equation
Phys. Rev. E 114, 014223 – Published 28 July, 2026
DOI: https://doi.org/10.1103/84mr-6nxm
Abstract
We systematically investigate the existence, stability, and dynamics of optical solitons in the framework of the one-dimensional nonlinear Schrödinger equation with the Riesz-fractional diffraction operator, cubic self-focusing, and linear loss, balanced by a linear parametric drive. The model, which can be realized in a laser cavity, produces standing and moving solitons, the latter ones existing below a critical velocity. One of the soliton species is stable in a wide range of parameters, while others are unstable. The fractional diffraction significantly alters the existence conditions and stability thresholds of the solitons. Collisions between moving solitons are considered too. The results essentially expand the variety of nonlinear modes in media with fractional diffraction.
