Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schrödinger equation with a PT-symmetric potential

Pengfei Li*, Boris A. Malomed, Dumitru Mihalache

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schrödinger equation with cubic or cubic–quintic (CQ) nonlinearity and a parity–time-symmetric potential, which may be realized in optical cavities. Solitons are destabilized at the bifurcation point, and, in the case of CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually conjugate branches of ghost states (GSs), with complex propagation constants, are created by the bifurcation, solely in the case of fractional diffraction. While GSs are not true solutions, direct simulations confirm that their shapes and results of their stability analysis provide a “blueprint” for the evolution of genuine localized modes in the system.

Original languageEnglish
Pages (from-to)3267-3270
Number of pages4
JournalOptics Letters
Volume46
Issue number13
DOIs
StatePublished - 1 Jul 2021

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