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On solutions to the string equation. (English) Zbl 1020.37579

Summary: The set of solutions to the string equation \([P,Q]=1\), where \(P\) and \(Q\) are differential operators is described.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics