Integrable ODEs on Associative Algebras
Abstract
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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2000
 DOI:
 10.1007/s002200050810
 arXiv:
 arXiv:solvint/9908004
 Bibcode:
 2000CMaPh.211..231M
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 19 pages, LaTeX