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research article
The Geometric Nature of the Flaschka Transformation
We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semisimple Lie algebras, the rigid body system on Toda orbits, and to coadjoint orbits of semidirect products groups. In addition, we develop an infinite-dimensional generalization for the group of area preserving diffeomorphisms of the annulus and apply it to the analysis of the dispersionless Toda lattice PDE and the solvable rigid body PDE.
Type
research article
Web of Science ID
WOS:000398836900002
Authors
Publication date
2017
Publisher
Published in
Volume
352
Issue
2
Start page
457
End page
517
Peer reviewed
REVIEWED
Written at
EPFL
EPFL units
Available on Infoscience
May 30, 2017
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