Complete integrability of derivative nonlinear Schrödinger-type equations. (English) Zbl 0936.37047
Summary: 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.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
