Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems . Most of these solutions are one dimensional . Using linear perturbation theory , expanded around such a one-dimensional solution , we find self-similar hydrodynamic solutions that are two- or three-dimensional . Since the deviation from a one-dimensional solution is small , we call these slightly two-dimensional and slightly three-dimensional self-similar solutions , respectively . As an example , we treat strong spherical explosions of the second type . A strong explosion propagates into an ideal gas with negligible temperature and density profile of the form \rho ( r, \theta, \phi ) = r ^ { - \omega } [ 1 + \sigma F ( \theta, \phi ) ] , where \omega > 3 and \sigma \ll 1 . Analytical solutions are obtained by expanding the arbitrary function F ( \theta, \phi ) in spherical harmonics . We compare our results with two dimensional numerical simulations , and find good agreement .