Integrable Hierarchies and Dispersionless Limit

Kanehisa Takasaki (Kyoto University); Takashi Takebe (University of Tokyo)

Integrable Hierarchies and Dispersionless Limit

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arxiv hep-th/9405096 v3 pith:ZRQHT6AU submitted 1994-05-16 hep-th nlin.SIsolv-int

Kanehisa Takasaki (Kyoto University) , Takashi Takebe (University of Tokyo) This is my paper · ORCID

classification hep-thnlin.SIsolv-int

keywords dispersionlesshierarchytodaconstructionhierarchiesdressingordinarysolutions

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Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is dressing operators of the ordinary KP and Toda hierarchy. An alternative construction of general solutions of the ordinary KP and Toda hierarchy is given as twistor construction which is quatization of the similar construction of solutions of dispersionless hierarchies. These results as well as those obtained in previous papers are presented with proofs and necessary technical details.

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Revisiting B\"acklund-Darboux transformations for KP and BKP integrable hierarchies
nlin.SI 2025-06 unverdicted novelty 4.0 of 10

Revisits Bäcklund-Darboux transformations for KP, BKP and related hierarchies in bilinear tau-function and fermionic operator frameworks, extending naturally to fully discrete cases.

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