Vector spatiotemporal localized structures in (3 $$+$$+ 1)-dimensional strongly nonlocal nonlinear media

We investigate the (3 $$+$$+ 1)-dimensional coupled nonlocal nonlinear Schrödinger equation in the inhomogeneous nonlocal nonlinear media and derive analytical vector spatiotemporal localized solution. Based on this solution, Gaussian solitons and some symmetric multipole patterns around the point $$(x, y) =(0,0)$$(x,y)=(0,0) can be constructed. The change trends of the amplitude and width of solitons are opposite, and they finally tend to a certain value. The compression and expansion of spatiotemporal localized structures are also studied in an exponential diffraction decreasing system.

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