# Quasi-classical limit of Toda hierarchy andW-infinity symmetries

@article{Takasaki1993QuasiclassicalLO, title={Quasi-classical limit of Toda hierarchy andW-infinity symmetries}, author={Kanehisa Takasaki and Takashi Takebe}, journal={Letters in Mathematical Physics}, year={1993}, volume={28}, pages={165-176} }

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…

## 62 Citations

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String equations of thepth generalized Kontsevich model and the compactifiedc=1 string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in…

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The 2D Toda hierarchy occupies a central position in the family of integrable hierarchies of the Toda type. The 1D Toda hierarchy and the Ablowitz–Ladik (aka relativistic Toda) hierarchy can be…

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The notion of string equations was discovered in the end of the eighties, and has been studied in the language of integrable hierarchies. String equations in the KP hierarchy are nowadays relatively…

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