Geodesic
Analytical Solution of the Rayleigh – Plesset Equation
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 1, pp. 3-13

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In this paper, we consider a mathematical model of the dynamics of the behavior of a spher- ically symmetric Rayleigh – Plesset bubble in the van der Waals gas model. The analysis of the model takes into account various isoprocesses without the presence of condensation and a model that takes into account condensation in an isothermal process. In each case, various character- istics are searched for, such as oscillation frequency (linear/small oscillations), damping factor, relaxation time, decrement, and logarithmic decrement. Solutions are found in quadratures for various parameters of the equation. The theoretical results obtained are compared with the results of the numerical solution of the Cauchy problem for various isoprocesses.
Keywords: nonlinear differential equations, small fluctuations, van der Waals equation, Rayleigh – Plesset equation
Mots-clés : exact solution 
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M. V. Gasanov; A. G. Gulkanov; K. A. Modestov. Analytical Solution of the Rayleigh – Plesset Equation. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 1, pp. 3-13. http://geodesic.mathdoc.fr/item/ND_2024_20_1_a0/