Spatiotemporal Hermite–Bessel solitons in (3+1)-dimensional strongly nonlocal nonlinear \(\varvec{\mathcal {PT}}\)-symmetric media

The propagation of optical solitons in the coupled dual waveguides with balanced gain and loss and nonlocal nonlinearity is governed by the coupled nonlocal nonlinear Schrodinger equation with \(\mathcal {PT}\)-symmetry. We study this model and obtain analytical spatiotemporal Hermite–Bessel soliton solutions. The control of expansion and compression of spatiotemporal Hermite–Bessel soliton in different axis directions are studied in the diffraction decreasing system. Moreover, the periodic compression and expansion of spatiotemporal Hermite–Bessel solitons in different axis directions are also discussed in the periodic distributed amplification system.