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Symmetries and exact solutions of the rotating shallow-water equations

Published online by Cambridge University Press:  14 August 2009

A. A. CHESNOKOV
A. A. CHESNOKOV*
Affiliation:
Lavrentyev Institute of Hydrodynamics and Novosibirsk State University, Novosibirsk 630090, Russia email: chesnokov@hydro.nsc.ru
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Abstract

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow-water equations can be transformed to the classical shallow-water model. The derived symmetries are used to generate new exact solutions of the rotating shallow-water equations. In particular, a new class of time-periodic solutions with quasi-closed particle trajectories is constructed and studied. The symmetry reduction method is also used to obtain some invariant solutions of the model. Examples of these solutions are presented with a brief physical interpretation.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 20 , Issue 5 , October 2009 , pp. 461 - 477
Copyright
Copyright © Cambridge University Press 2009

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