Complete integrability of derivative nonlinear Schrödinger-type equations

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We study matrix generalizations of derivative nonlinear Schrödinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.
14 pages, LaTeX2e (IOP style), to appear in Inverse Problems

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