Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schr\"odinger equations

TL;DR

This paper investigates higher-dimensional PT-symmetric nonlinear Schrödinger equations with generalized potentials, revealing conditions for stable solitons, their propagation, and transformation, advancing understanding of PT-symmetric optical systems.

Contribution

It introduces a class of PT-symmetric potentials supporting exact solitons in multiple dimensions and analyzes their stability, propagation, and manipulation, which is a novel extension in the field.

Findings

Stable fundamental solitons exist in the model.

Higher-order solitons are generally unstable.

Stable solitons can be manipulated via potential variations.

Abstract

We study a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials, which can support exact solitons in one- and multi-dimensional nonlinear Schr\"odinger equation. In the 1D and multi-D settings, we find that a properly adjusted localization parameter may support fully real energy spectra. Also, continuous families of fundamental and higher-order solitons are produced. The fundamental states are shown to be stable, while the higher-order ones, including 1D multimodal solitons, 2D solitons, and 3D light bullets, are unstable. Further, we find that the stable solitons can always propagate, in a robust form, remaining trapped in slowly moving potential wells of the GS-II type, which opens the way for manipulations of optical solitons. Solitons may also be transformed into stable forms by means of adibatic variation of potential parameters. Finally, an alternative type of n-dimensional PT-symmetric GS-II potentials is reported too. These results will be useful to further explore the higher-dimensional PT-symmetric solitons and to design the relative physical experiments.