Gray solitons in parity-time-symmetric localized potentials with fractional-order diffraction

Abstract

The properties of existence and stability of gray solitons in parity-time (PT)-symmetric localized potentials with fractional-order diffraction are studied. This system can support stable gray solitons. The influences of the Lévy index and the real and imaginary parts of the complex potentials on existence, stability, and grayness of these solitons are carefully investigated. Especially, if some coefficients of PT-symmetric potentials in nonlinear fractional Schrödinger equation are changed, the transition between gray soliton and anti-dark soliton will occur. In addition, we also discuss the transverse energy flow in the gray and anti-dark solitons with fractional-order diffraction.