Spatiotemporal localizations in \[(3+1)\] -dimensional \[{{\mathcal {PT}}}\] -symmetric and strongly nonlocal nonlinear media

Abstract

A \[(3+1)\]-dimensional coupled nonlocal nonlinear Schrödinger equation in the inhomogeneous \[{\mathcal {PT}}\]-symmetric and strongly nonlocal nonlinear media is studied, and analytical vector spatiotemporal localized solutions are obtained. From these solutions, Gaussian soliton clusters, multipole soliton clusters, and nested soliton clusters can be constructed. The expansion behavior and periodic expansion and compression of spatiotemporal localizations are also investigated in the diffraction decreasing system and periodic modulation system, respectively.