Commutator identities on associative algebras and integrability of nonlinear pde's

Details Commutator identities on associative algebras and integrability of nonlinear pde's Commutator identities on associative algebras and integrability of nonlinear pde's

2007-03-11

arxiv.org/abs/nlin/0703018v1

Theor.Math.Phys.154:405-417,2008

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages

Scientific paper

10.1007/s11232-008-0035-6

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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