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A class of integrable evolutionary vector equations. (English) Zbl 1178.37068
Theor. Math. Phys. 142, No. 1, 8-14 (2005); translation from Teor. Mat. Fiz. 142, No. 1, 13-20 (2005).
Summary: We present the results of classifying integrable evolutionary $$N$$-component vector equations and construct Bäcklund transformations for each equation as proof of the exact integrability.

##### MSC:
 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35Q53 KdV equations (Korteweg-de Vries equations)
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