Multi-dimensional stable fundamental solitons and excitations in [formula omitted]-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions

Abstract

We demonstrate the parity-time- (PT-) symmetric harmonic-Gaussian potential with unbounded gain-and-loss distribution can support entirely-real linear spectra, stable spatial and spatio-temporal solitons in an inhomogeneous nonlinear medium (e.g., cubic nonlinear Schrödinger equation with the self-focusing and defocusing cases). Exact analytical solitons are derived in both one-dimensional (1D) and higher-dimensional (e.g., 2D, 3D) geometries such that they are verified to be stable in the given parameters regions. Particularly, several families of numerical fundamental solitons (especially the 1D double-peaked solitons, 2D vortex solitons, and 3D double bullets) can be found to be stable around the propagation parameters for exact solitons. Other significant properties of solitons are also explored including the interactions of solitons, stable soliton excitations, and transverse power flows. The results may excite the corresponding theoretical analysis and experiment designs.