Quasi-classical limit of Toda hierarchy andW-infinity symmetries
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Previous results on quasi-classical limit of the KP hierarchy and itsW-infinity symmetries are extended to the Toda hierarchy. The Planck constantħ now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions, and tau function, are redefined.W1 + ∞ symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted tow1 + ∞ symmetries of the dispersionless hierarchy through their action on the tau function.
Mathematics Subject Classifications (1991)17B65 35Q58 58F07
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