Dear Sir. Regarding your question about the analytical methods that can solve Rayleigh-Plesset equation in bubble dynamics field. Several canonical results in bubble dynamics, including the Rayleigh collapse time, the Rayleigh-Plesset equation, and the Minnaert frequency have been re-derived. in arbitrary dimension. The bubbles generally display faster dynamics in higher dimensions, as the natural period and collapse time both decrease. Particularly, the late-time collapse behavior of a bubble is much stronger in higher dimensions. The normalized collapse equation and its analytic approximation were examined in higher dimensions, suggesting a choice of boundary conditions upon which to base the approximations. For more details the following below links may help you in your analysis:

http://doc.utwente.nl/50316/1/rayleigh-plesset.pdf

http://arxiv.org/pdf/1206.5753.pdf

http://authors.library.caltech.edu/25021/1/chap4.pdf

Thanks