A description of Lax type integrable dynamical systems via the MarsdenaWeinstein reduction method

A Lie-algebraic approach to constructing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the MarsdenaWeinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well known...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2013-09, Vol.18 (9), p.2295-2303
Main Author: Prykarpatsky, Yarema A
Format: Article
Language:English
Subjects:
Computer simulation
Dynamical systems
Group theory
Manifolds
Mathematical models
Nonlinearity
Reduction
Symmetry
Online Access:Get full text
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Summary:A Lie-algebraic approach to constructing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the MarsdenaWeinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well known AdleraKostantaSouriauaBerezinaKirillov method and the associated R-matrix approach is analyzed.
ISSN:1007-5704