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.

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Cited by in corpus (7)

• Analytical solutions for problems of bubble dynamics
• On the criteria for integrability of the Liénard equation
• Evolution of spherical cavitation bubbles: parametric and closed-form solutions
• 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