On a Novel Resonant Ermakov-NLS System: Painlevé Reduction

Colin Rogers () and Wolfgang K. Schief ()
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Colin Rogers: The University of New South Wales, School of Mathematics and Statistics and Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems
Wolfgang K. Schief: The University of New South Wales, School of Mathematics and Statistics and Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 1081-1098 from Springer

Abstract: Abstract 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_49

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DOI: 10.1007/978-3-319-72456-0_49

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