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 previously been obtained. 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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- October 2014
- DOI:
- 10.1088/1751-8113/47/40/405202
- arXiv:
- arXiv:1409.6699
- Bibcode:
- 2014JPhA...47N5202K
- Keywords:
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- Physics - Fluid Dynamics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- J. Phys. A: Math. Theor. 47 405202 (2014)