Kudryashov and Sinelshchikov’s method for solving the radial oscillation problem of multielectron bubbles in liquid helium

This work investigates the exact general analytical solution of the Rayleigh equation for multielectron bubbles in liquid helium using Kudryashov and Sinelshchikov’s method. We firstly obtain its first integral involving three negative exponential powers, then a specific Sundman transformation is pr...

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Bibliographic Details
Published in:Journal of mathematical chemistry 2020-08, Vol.58 (7), p.1481-1488
Main Authors: Qin, Yupeng, Lou, Qingjun, Wang, Zhen, Zou, Li
Format: Article
Language:English
Subjects:
Algorithms
Bubbles
Chemistry
Chemistry and Materials Science
Elliptic functions
Exact solutions
Helium
Liquid helium
Math. Applications in Chemistry
Mathematical analysis
Numerical analysis
Original Paper
Physical Chemistry
Rayleigh equations
Theoretical and Computational Chemistry
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Summary:This work investigates the exact general analytical solution of the Rayleigh equation for multielectron bubbles in liquid helium using Kudryashov and Sinelshchikov’s method. We firstly obtain its first integral involving three negative exponential powers, then a specific Sundman transformation is proper established to transform it into an equation for the elliptic functions, and finally the analytical solution expressed by Weierstrass elliptic function is constructed appropriately. As applications, the derived analytical solution is used to test numerical algorithm, and also to construct the analytical expressions of the bubble oscillation period and the derivatives of the bubble radius. Further, the influence of the pressure on the helium is also discussed.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-020-01145-y