Analysis on the Integrability of the Rayleigh-Plesset Equation with Painlev\'e Test and Lie Symmetry Groups

Abstract

The Rayleigh-Plesset equation (RPE) is a nonlinear ordinary differential equation (ODE) of second order that governs the dynamics of a spherical bubble and plays an essential role in interpreting many real-world phenomena involving the presence of bubbles in engineering and medical fields. In the present paper, we present a relatively comprehensive analysis of the analytical solutions of the RPE. The integrability of the Rayleigh-Plesset equation is investigated and discussed using the Painlev\'e test. Lie symmetry groups are employed subsequentially to obtain several exact solutions to the simplified Rayleigh-Plesset equations.