On Ermakov–Painlevé II systems. Integrable reduction

On Ermakov–Painlevé II systems. Integrable reduction

Novel hybrid Ermakov–Painlevé II systems are introduced and those with underlying integrable structure delimited. The Ermakov invariant is used to construct an algorithmic solution procedure which involves both the isolation of positive solutions Σ of Painlevé XXXIV and the integration of Σ - 1 . Th...

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Veröffentlicht in:Meccanica (Milan) 2016-12, Vol.51 (12), p.2967-2974
Hauptverfasser: Rogers, Colin, Schief, Wolfgang K.
Format: Artikel
Sprache:eng
Schlagworte:
50th Anniversary of Meccanica
Algorithms
Automotive Engineering
Civil Engineering
Classical Mechanics
Construction
Hybrid systems
Invariants
Joints
Mechanical Engineering
Physics
Physics and Astronomy
Reduction
Transformations
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Zusammenfassung:Novel hybrid Ermakov–Painlevé II systems are introduced and those with underlying integrable structure delimited. The Ermakov invariant is used to construct an algorithmic solution procedure which involves both the isolation of positive solutions Σ of Painlevé XXXIV and the integration of Σ - 1 . The Bäcklund transformation admitted by Painlevé II is applied iteratively in this connection.
ISSN:0025-6455
1572-9648
DOI:10.1007/s11012-016-0546-4