dorsal/arxiv
View SchemaIntegrable ODEs on Associative Algebras
| Authors | A. V. Mikhailov, V. V. Sokolov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9908004 |
| URL | https://arxiv.org/abs/solv-int/9908004 |
| DOI | 10.1007/s002200050810 |
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.
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"abstract": "In this paper we give definitions of basic concepts such as symmetries, first\nintegrals, Hamiltonian and recursion operators suitable for ordinary\ndifferential equations on associative algebras, and in particular for matrix\ndifferential equations. We choose existence of hierarchies of first integrals\nand/or symmetries as a criterion for integrability and justify it by examples.\nUsing our componentless approach we have solved a number of classification\nproblems for integrable equations on free associative algebras. Also, in the\nsimplest case, we have listed all possible Hamiltonian operators of low order.",
"arxiv_id": "solv-int/9908004",
"authors": [
"A. V. Mikhailov",
"V. V. Sokolov"
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"doi": "10.1007/s002200050810",
"title": "Integrable ODEs on Associative Algebras",
"url": "https://arxiv.org/abs/solv-int/9908004"
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