 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ΟΜΜ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| A.G. Petrov, "The stability of capillary waves of finite amplitude," J. Appl. Math. Mech. 81 (4), 317-324 (2017) |
| Year |
2017 |
Volume |
81 |
Issue |
4 |
Pages |
317-324 |
| DOI |
10.1016/j.jappmathmech.2017.12.009 |
| Title |
The stability of capillary waves of finite amplitude |
| Author(s) |
A.G. Petrov (Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia, petrovipmech@gmail.com) |
| Abstract |
Stability (in the sense of a relaxed definition of Lyapunov stability) of Crapper's exact solution for capillary waves is proven by Lyapunov's direct method. The wave surface is described using coefficients of the Laurent series of the conformal mapping of one period of the wave onto the unit circle interior (the Stokes coefficients). The Stokes coefficients are treated as generalized wave coordinates. The dynamical equations for a capillary wave are represented in the form of an infinite chain of Euler-Lagrange equations for the Stokes coefficients. A steady solution is found for these equations, and it is found to be the Crapper solution for capillary waves. The Lyapunov function is constructed basing on the energy and momentum conservation laws, and it is shown that it is positive definite with respect to arbitrary perturbations of the wave surface with period equal to the wavelength. |
| Received |
05 May 2016 |
| Link to Fulltext |
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