Robust three-dimensional spatial soliton clusters in strongly nonlocal media

The propagation of three-dimensional soliton clusters in strongly nonlocal nonlinear media is investigated analytically and numerically. A broad class of exact self-similar solutions to the strongly nonlocal Schrödinger equation has been obtained. We find robust soliton cluster solutions, constructed with the help of Whittaker and Hermite-Gaussian functions. We confirm the stability of these solutions by direct numerical simulation. Our results demonstrate that robust higher-order spatial soliton clusters can exist in various forms, such as three-dimensional Gaussian solitons, radially symmetric solitons, multipole solitons and shell solitons.