Ermakov–Ray–Reid Systems in (2+1)‐Dimensional Rotating Shallow Water Theory

Abstract

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.