Integrable Hierarchies and Dispersionless Limit

Details Integrable Hierarchies and Dispersionless Limit Integrable Hierarchies and Dispersionless Limit

1994-05-16

arxiv.org/abs/hep-th/9405096v3

Rev.Math.Phys. 7 (1995) 743-808

Physics

High Energy Physics

High Energy Physics - Theory

63 pages, University of Tokyo preprint, UTMS 94-35. (AMS TeX ver.2.1) (Typos are corrected and references are added.)

Scientific paper

10.1142/S0129055X9500030X

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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