Integrable ODEs on Associative Algebras

Details Integrable ODEs on Associative Algebras Integrable ODEs on Associative Algebras

1999-08-06

arxiv.org/abs/solv-int/9908004v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, LaTeX

Scientific paper

10.1007/s002200050810

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.

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