Fundamental solitons and dynamical analysis in the defocusing Kerr medium and $$\varvec{\mathcal {PT}}$$ PT -symmetric rational potential

Abstract

We find that a class of parity-time- ( $$\mathcal {PT}$$ -) symmetric rational potentials can support stable solitons in the defocusing Kerr-nonlinear media, though they may not enjoy entirely real linear spectra. Analytical expressions of spatial solitons are elicited at lots of isolated propagation-constant points, around which several families of numerical fundamental solitons can be found to be stable, which is validated by linear stability analysis and nonlinear wave propagation. Many other intriguing properties of nonlinear localized modes are also discussed in detail, including the interactions, excitations, and transverse power flows. The idea of the $$\mathcal {PT}$$ -symmetric rational potentials can also be extended to other types of nonlinear wave models.