MODIFIED ALGEBRAIC STRUCTURES FOR SOME COMPLETELY INTEGRABLE SYSTEMS

2001 ◽  
Vol 16 (38) ◽  
pp. 2457-2462
Author(s):  
STANISŁAW P. KASPERCZUK
Keyword(s):  
Hamiltonian Systems ◽  
Quantum Groups ◽  
Algebraic Structure ◽  
Integrable Systems ◽  
Algebraic Structures ◽  
Completely Integrable Systems ◽  
Integrable Hamiltonian Systems ◽  
Completely Integrable ◽  
Completely Integrable Hamiltonian Systems

We modify the algebraic structure of a Poisson bialgebra by considering the deformed coproduct [Formula: see text] and deformations of an algebra e(2). These modifications lead to the quantum groups and provide new classes of completely integrable Hamiltonian systems.

FLAT CONNECTIONS AND INTEGRABLE SYSTEMS

1989 ◽  
Vol 03 (02) ◽  
pp. 211-233
Author(s):  
D. H. SATTINGER
Keyword(s):  
Lie Algebras ◽  
Integrable Systems ◽  
Scattering Theory ◽  
Completely Integrable Systems ◽  
Integrable Hamiltonian Systems ◽  
Flat Connections ◽  
Gauge Transformations ◽  
First Order ◽  
Completely Integrable ◽  
Completely Integrable Hamiltonian Systems

The theory of completely integrable systems based on n × n first order isospectral problems is reviewed. The topics discussed are the inverse scattering theory for n × n systems; hierarchies of completely integrable Hamiltonian systems based on semi-simple Lie algebras; flat connections and gauge transformations; and the gauge theory of Bäcklund transformations.

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