Lie groups, differential geometry, and nonlinear integrable systems

2019 ◽  
pp. 321-336
Author(s):  
A. V. Razumov ◽  
M. V. Saveliev
Keyword(s):  
Differential Geometry ◽  
Lie Groups ◽  
Integrable Systems

scholarly journals ON LIE GROUPS, CLUSTER VARIABLES AND INTEGRABLE SYSTEMS

2013 ◽  
Vol 28 (03n04) ◽  
pp. 1340007
Author(s):  
A. MARSHAKOV
Keyword(s):  
Lie Groups ◽  
Integrable Systems ◽  
Explicit Construction ◽  
Integrable Models ◽  
Loop Groups ◽  
Integrals Of Motion ◽  
General Terms

We propose an explicit construction for the integrable models on Poisson submanifolds of the Lie groups. The integrals of motion are computed in cluster variables via the Lax map. This generalized construction for the co-extended loop groups allows to formulate, in general terms, some new classes of integrable models.

scholarly journals Lie-group methods

Acta Numerica ◽  
2000 ◽  
Vol 9 ◽  
pp. 215-365 ◽  
Author(s):  
Arieh Iserles ◽  
Hans Z. Munthe-Kaas ◽  
Syvert P. Nørsett ◽  
Antonella Zanna
Keyword(s):  
Differential Geometry ◽  
Differential Equations ◽  
Lie Groups ◽  
Lie Group ◽  
Group Structure ◽  
Practical Interest ◽  
The Novel ◽  
Group Methods ◽  
Novel Theory ◽  
Numerical Integrators

Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively correct geometry and dynamics and in the minimization of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, highlighting theory, algorithmic issues and a number of applications.

Sign in / Sign up

Export Citation Format

Share Document