On a Novel Resonant Ermakov-NLS System: Painlevé Reduction

  • Colin Rogers
  • Wolfgang K. SchiefEmail author


A novel resonant Ermakov-NLS system is introduced which admits symmetry reduction to a hybrid Ermakov-Painlevé 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 Painlevé 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 Bäcklund transformation admitted by the canonical Painlevé II equation.


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Authors and Affiliations

  1. 1.School of Mathematics and Statistics and Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex SystemsThe University of New South WalesSydneyAustralia

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