More recently,  analytical closed-form solutions were found  for the Rayleigh–Plesset equation for both an empty and gas-filled bubble   and were generalized to the N-dimensional case. The case when the surface tension is present due to the effects of capillarity were also studied.
Also, for the special case where surface tension and viscosity are neglected, high-order analytical approximations are also known.
In the static case, the Rayleigh–Plesset equation simplifies, yielding the Young–Laplace equation:
When only infinitesimal periodic variations in the bubble radius and pressure are considered, the RP equation also yields the expression of the natural frequency of the bubble oscillation.