On multi-component Ermakov systems in a two-layer fluid: a variational approach

By introducing Madelung-type transformations, a two-layer fluid model with a circular paraboloidal bottom topography is reduced to coupled nonlinear Schrodinger equations incorporating harmonic traps and de Broglie-Bohm quantum potentials. A kind of multi-component Ermakov system is obtained via a variational approach and a multi-parameter Gaussian ansatz. In particular, three typical reductions to generalized Ermakov systems are discussed. Notable integrals of motion and additional Hamiltonian structures are employed to derive analytical solutions in terms of elliptic integrals for the multi-component Ermakov systems.