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Quiescent and traveling solitons in the fractional parametrically driven damped nonlinear Schrödinger equation

Dongdong Wang1,2, Rujiang Li3, David Laroze4, Boris A. Malomed4,5, and Pengfei Li1,2,*

  • 1Department of Physics, Taiyuan Normal University, Jinzhong 030619, China
  • 2Institute of Computational and Applied Physics, Taiyuan Normal University, Jinzhong 030619, China
  • 3National Key Laboratory of Radar Detection and Sensing, School of Electronic Engineering, Xidian University, Xi'an 710071, China
  • 4Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
  • 5Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel

  • *Contact author: lpf281888@gmail.com
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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.

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Phys. Rev. E 114, 014223– Published 28 July, 2026
  • Received 24 March 2026
  • Accepted 13 July 2026
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