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

TL;DR

This paper investigates the integrability of the Rayleigh-Plesset equation using Painlevé test and Lie symmetry groups, providing insights into its analytical solutions relevant to engineering and medical applications.

Contribution

It offers a comprehensive analysis of the Rayleigh-Plesset equation's integrability and derives exact solutions using symmetry methods, advancing understanding of bubble dynamics.

Findings

Painlevé test indicates conditions for integrability.

Lie symmetry groups yield exact solutions.

Enhanced understanding of bubble dynamics in applications.

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.