Ermakov–Ray–Reid Systems in (2+1)-Dimensional Rotating Shallow Water Theory
A (2+1)-dimensional rotating shallow water system with an underlying circular paraboloidal bottom topography is shown to admit a multiparameter integrable nonlinear subsystem of Ermakov–Ray–Reid type. The latter system, which describes the time evolution of the semi-axes of the elliptical moving shoreline on the paraboidal basin, is also Hamiltonian. The complete solution of the generic eight-dimensional dynamical system governing the reduction is obtained in terms of an elliptic integral representation.
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Document Type: Research Article
Affiliations: 1: The Hong Kong Polytechnic University 2: The University of New South Wales
Publication date: October 1, 2010