Integrable ODEs on Associative Algebras
solv-int
2009-10-31 v1 可精确求解与可积系统
摘要
In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamiltonian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential equations. We choose existence of hierarchies of first integrals and/or symmetries as a criterion for integrability and justify it by examples. Using our componentless approach we have solved a number of classification problems for integrable equations on free associative algebras. Also, in the simplest case, we have listed all possible Hamiltonian operators of low order.
引用
@article{arxiv.solv-int/9908004,
title = {Integrable ODEs on Associative Algebras},
author = {A. V. Mikhailov and V. V. Sokolov},
journal= {arXiv preprint arXiv:solv-int/9908004},
year = {2009}
}
备注
19 pages, LaTeX