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 Schr?dinger 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.
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Zhong et al. (2008) studied this question.
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