Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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M.B. Kochanov, N.A. Kudryashov, and D.I. Sinel'shchikov, "Non-linear waves on shallow water under an ice cover. Higher order expansions," J. Appl. Math. Mech. 77 (1), 25-32 (2013)
Year 2013 Volume 77 Issue 1 Pages 25-32
Title Non-linear waves on shallow water under an ice cover. Higher order expansions
Author(s) M.B. Kochanov (Moscow, Russia,
N.A. Kudryashov (Moscow, Russia)
D.I. Sinel'shchikov (Moscow, Russia)
Abstract Non-linear wave processes on the surface of shallow water under a layer of ice are considered taking bending deformations and tension compression into account. A closed system of equations in the water level perturbations and the velocity potential is derived to describe them. From the consistancy conditions for this system, using the method of multiple scales and perturbation theory, a ninth-order non-linear evolution equation is obtained for describing the perturbations of the water level, taking into account higher order corrections in the small parameters. A periodic solution of the equation obtained is constructed, expressed in terms of Weierstrass elliptic functions. Solutions are obtained in the form of solitary waves, expressed in terms of hyperbolic functions, using a modification of the simplest equations method. It is shown that, for periodic and solitary waves, two forms of wave profiles exist depending on the parameters of the mathematical model.
Received 28 February 2012
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