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.VI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.