Analytical solutions of the Rayleigh equation for empty and gas--filled bubble

Abstract

The Rayleigh equation for bubble dynamics is widely used. However, analytical solutions of this equation have not been obtained previously. Here we find closed--form general solutions of the Rayleigh equation both for an empty and gas--filled spherical bubble. We present an approach allowing us to construct exact solutions of the Rayleigh equation. We show that our solutions are useful for testing numerical algorithms.

References in corpus (3)

• The Quest for the Most Spherical Bubble
• Analytical Approximations for the Collapse of an Empty Spherical Bubble
• Linearization of Second-Order Ordinary Differential Equations by Generalized Sundman Transformations

Cited by in corpus (6)

• Analytical solutions for problems of bubble dynamics
• On the criteria for integrability of the Liénard equation
• On connections of the Liénard equation with some equations of Painlevé--Gambier type
• The Rayleigh collapse of two spherical bubbles
• Generalized and new solutions of the NRT nonlinear Schrödinger equation
• From Cavitation to Astrophysics: Explicit Solution of the Spherical Collapse Equation