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Quasiclassical limit of KP hierarchy, \(W\)-symmetries, and free fermions. (English. Russian original) Zbl 0947.37038

J. Math. Sci., New York 94, No. 4, 1635-1641 (1999); translation from Zap. Nauchn. Semin. POMI 235, 295-303 (1996).
The dispersionless KP hierarchy from the point of view of quasi-classical limit is investigated. Its Lax formalism, W-infinity symmetries and general solutions are shown to be reproduced from their counterparts in the KP hierarchy in the limit of \(\hbar \to 0\). Free fermions and bosonized vertex operators play a key role in the description of W-infinity symmetries and general solutions, which is technically very similar to a recent free fermion formalism of \(c=1\) matrix models.

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)
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

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