A general algorithm is proposed to obtain "shift elements" which are used to construct inhomogeneous Lax operators containing constant terms, and satisfying general linear r-matrix algebra with a non-dynamical classical r-matrix. The proposed construction is illustrated by examples of skew-symmetric rational, non-skew-symmetric "Z p-graded" and "anisotropic irrational" r-matrices for several known classes of Lax operators and integrable systems, such as rational Gaudin systems in an external magnetic field, closed and open Toda chains, and Kovalevskaja and Zhukovski-Volterra integrable systems. New Lax operators and new integrable systems are also described, associated with "anisotropic irrational" r-matrices that generalize Zhukovski-Volterra integrable systems for the Lie algebra cases g l (n) and s o (n) © 2014 Elsevier B.V

Skrypnyk, T. (2014). Generalized shift elements and classical r-matrices: Construction and applications. JOURNAL OF GEOMETRY AND PHYSICS, 80, 71-87 [10.1016/j.geomphys.2013.12.011].

Generalized shift elements and classical r-matrices: Construction and applications

Skrypnyk, T.
2014

Abstract

A general algorithm is proposed to obtain "shift elements" which are used to construct inhomogeneous Lax operators containing constant terms, and satisfying general linear r-matrix algebra with a non-dynamical classical r-matrix. The proposed construction is illustrated by examples of skew-symmetric rational, non-skew-symmetric "Z p-graded" and "anisotropic irrational" r-matrices for several known classes of Lax operators and integrable systems, such as rational Gaudin systems in an external magnetic field, closed and open Toda chains, and Kovalevskaja and Zhukovski-Volterra integrable systems. New Lax operators and new integrable systems are also described, associated with "anisotropic irrational" r-matrices that generalize Zhukovski-Volterra integrable systems for the Lie algebra cases g l (n) and s o (n) © 2014 Elsevier B.V
Articolo in rivista - Articolo scientifico
Classical r-matrices; Integrable systems; Lax operators; Mathematical Physics; Physics and Astronomy (all); Geometry and Topology
English
2014
80
71
87
none
Skrypnyk, T. (2014). Generalized shift elements and classical r-matrices: Construction and applications. JOURNAL OF GEOMETRY AND PHYSICS, 80, 71-87 [10.1016/j.geomphys.2013.12.011].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/227430
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