Algebraic and differential geometric aspects of the integrability of nonlinear dynamical systems on infinite-dimensional functional manifolds
Identifieur interne : 000714 ( Istex/Curation ); précédent : 000713; suivant : 000715Algebraic and differential geometric aspects of the integrability of nonlinear dynamical systems on infinite-dimensional functional manifolds
Auteurs : Anatoliy K. Prykarpatsky [Pologne, Ukraine] ; Ihor V. Mykytiuk [Ukraine]Source :
- Mathematics and Its Applications ; 1998.
Abstract
Abstract: Lie algebraic ideals, as is well known, are widely used in the modern theory of smooth integrable dynamical systems on manifolds. Using them one has succeeded in the classification of many nonlinear dynamical systems whose complete integrability was stated before by means of different mathematical techniques (Fushchych et al., 1990). For the last few years the special attention has been paid to nonlinear dynamical systems that also possess the Lax type isospectrality property (Novikov, 1980), (Holod et al., 1992), (Takhtadjian et al., 1987), (Newell, 1985). We focus on their description below, although our treatment will not be entirely complete. Here our aim is to single out the main mathametical content of the theory of the integrability of nonlinear dynamical systems, which is universal in the sense that it applies to almost all such systems.
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DOI: 10.1007/978-94-011-4994-5_5
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