On integrability of Hirota-Kimura type discretizations
Matteo Petrera, Andreas Pfadler, Yuri B. Suris
TL;DR
This paper reviews the integrability properties of Hirota-Kimura discretizations applied to algebraically completely integrable systems with quadratic vector fields, highlighting the underlying mechanisms and summarizing current results.
Contribution
It provides a comprehensive overview of the integrability of Hirota-Kimura discretizations and introduces the concept of Hirota-Kimura bases for these systems.
Findings
List of integrable systems discretized by Hirota-Kimura method
Description of the Hirota-Kimura bases mechanism
Summary of current results on integrability
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.
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