A combinatorial approach to integrals of Kahan-Hirota-Kimura discretizations
Ren\'e Zander
TL;DR
This paper introduces a combinatorial method to analyze formal integrals of motion for Kahan-Hirota-Kimura discretizations, providing a proof for a known integral formula in specific Hamiltonian systems.
Contribution
It presents a novel combinatorial approach to study integrals of motion in Kahan-Hirota-Kimura discretizations, extending understanding of their structure in cubic Hamiltonian systems.
Findings
Provided a combinatorial proof of the integral formula
Extended the analysis to symplectic and Poisson vector spaces
Confirmed the existence of formal integrals of motion in the studied systems
Abstract
We consider an Ansatz for the study of the existence of formal integrals of motion for Kahan-Hirota-Kimura discretizations. In this context, we give a combinatorial proof of the formula of Celledoni-McLachlan-Owren-Quispel for an integral of motion of the discretization in the case of cubic Hamiltonian systems on symplectic vector spaces and Poisson vector spaces with constant Poisson structure.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons