On integrability of Hirota-Kimura type discretizations

Abstract

We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.

47 pages, some minor changes

References in corpus (2)

• An integrable discretization of the rational su(2) Gaudin model and related systems
• Hirota-Kimura Type Discretization of the Classical Nonholonomic Suslov Problem

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