Abstract
We show that commutator identities on associative algebras generate solutions of the linearized versions of integrable equations. In addition, we introduce a special dressing procedure in a class of integral operators that allows deriving both the nonlinear integrable equation itself and its Lax pair from such a commutator identity. The problem of constructing new integrable nonlinear evolution equations thus reduces to the problem of constructing commutator identities on associative algebras.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 477–491, March, 2008.
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Pogrebkov, A.K. Commutator identities on associative algebras and the integrability of nonlinear evolution equations. Theor Math Phys 154, 405–417 (2008). https://doi.org/10.1007/s11232-008-0035-6
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DOI: https://doi.org/10.1007/s11232-008-0035-6