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Ermakov–Ray–Reid Systems in (2+1)‐Dimensional Rotating Shallow Water Theory
Author(s) -
Rogers Colin,
An Hongli
Publication year - 2010
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2010.00488.x
Subject(s) - integrable system , hamiltonian system , nonlinear system , hamiltonian (control theory) , waves and shallow water , classical mechanics , geometry , mathematics , mathematical physics , physics , mathematical analysis , quantum mechanics , mathematical optimization , thermodynamics
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.