Analytical solutions for problems of bubble dynamics

Abstract

Recently, an asymptotic solution of the Rayleigh equation for an empty bubble in $N$ dimensions has been obtained. Here we give the closed--from general analytical solution of this equation. We also find the general solution of the Rayleigh equation in $N$ dimensions for the case of a gas--filled hyperspherical bubble. In addition, we include a surface tension into consideration.

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• On connections of the Liénard equation with some equations of Painlevé--Gambier type
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• Generalized and new solutions of the NRT nonlinear Schrödinger equation
• Superfluid Rayleigh-Plesset extension of FLRW cosmology
• From Cavitation to Astrophysics: Explicit Solution of the Spherical Collapse Equation
• Solution to the one-dimensional Rayleigh-Plesset equation by the Differential Transform method
• Mapping Driven Oscillations in the Size of a Bubble to the Dynamics of a Newtonian Particle in a Potential
• Analysis on the Integrability of the Rayleigh-Plesset Equation with Painlevé Test and Lie Symmetry Groups