Multi-component Ermakov Systems: Structure and Linearization

A symmetry reduction of a 2q1.-dimensional nonlinear N-layer fluid model is shown to lead to a prototype for an N-component extension of the classical Ermakov system. The general N-component Ermakov system introduced here has the attractive property that it may be iteratively reduced to a system of Ny2 linear equations augmented by a canonical 2-component Ermakov system. The recently established linearization procedure for the latter may then be used to solve the N-component system N)2 in generality. The procedure is illustrated, in detail, for a 3-component system. Sequences of classical 2-component Ermakov systems are shown to be linked via Darboux transformations.