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Journal of Applied Mathematics
Volume 2012, Article ID 591058, 20 pages
http://dx.doi.org/10.1155/2012/591058
Research Article

Homotopy Analysis Method for the Rayleigh Equation Governing the Radial Dynamics of a Multielectron Bubble

1Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Ciudad Universitaria, Coyoacán 04510, México, DF, Mexico
2Facultad de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, Coyoacán 04510, México, DF, Mexico
3Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, Coyoacán 04510, México, DF, Mexico

Received 29 March 2012; Accepted 15 August 2012

Academic Editor: Hui-Shen Shen

Copyright © 2012 F. A. Godínez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The homotopy analysis method is used to obtain analytical solutions of the Rayleigh equation for the radial oscillations of a multielectron bubble in liquid helium. The small order approximations for amplitude and frequency fit well with those computed numerically. The results confirm that the homotopy analysis method is a powerful and manageable tool for finding analytical solutions of strongly nonlinear dynamical systems.