On a Novel Resonant Ermakov-NLS System: Painlevé Reduction

A novel resonant Ermakov-NLS system is introduced which admits symmetry reduction to a hybrid Ermakov-Painleve II system. If the latter is Hamiltonian then combination with a characteristic Ermakov invariant provides an algorithmic integration procedure. The latter involves the isolation of positive solutions of a concomitant integrable Painleve XXXIV equation. Explicit expressions for a multi-parameter class of wave packet representations for the original Ermakov-NLS system are obtained via the iterated application of a Backlund transformation admitted by the canonical Painleve II equation.