Geodesic
Commutator identities on associative algebras and the integrability of
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 3, pp. 477-491

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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.
Keywords: nonlinear evolution equation
Mots-clés : Lax pair. 
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     author = {A. K. Pogrebkov},
     title = {Commutator identities on associative algebras and the integrability of},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {477--491},
     publisher = {mathdoc},
     volume = {154},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a4/}
}
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A. K. Pogrebkov. Commutator identities on associative algebras and the integrability of. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 3, pp. 477-491. http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a4/