Commutator identities on associative algebras and integrability of nonlinear pde's
Exactly Solvable and Integrable Systems
2008-11-26 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
It is shown that commutator identities on associative algebras generate solutions of linearized integrable equations. Next, a special kind of the dressing procedure is suggested that in a special class of integral operators enables to associate to such commutator identity both nonlinear equation and its Lax pair. Thus problem of construction of new integrable pde's reduces to construction of commutator identities on associative algebras.
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Cite
@article{arxiv.nlin/0703018,
title = {Commutator identities on associative algebras and integrability of nonlinear pde's},
author = {A. K. Pogrebkov},
journal= {arXiv preprint arXiv:nlin/0703018},
year = {2008}
}
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12 pages