Kadomtsev–Petviashvili Turning Points and CKP Hierarchy

A characterization of the Kadomtsev–Petviashvili hierarchy of type C (CKP) in terms of the KP tau-function is given. Namely, we prove that the CKP hierarchy can be identified with the restriction of odd times flows of the KP hierarchy on the locus of turning points of the second flow. The notion of...

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Bibliographic Details
Published in:Communications in mathematical physics 2021-09, Vol.386 (3), p.1643-1683
Main Authors: Krichever, I., Zabrodin, A.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Fixed points (mathematics)
Mathematical analysis
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:A characterization of the Kadomtsev–Petviashvili hierarchy of type C (CKP) in terms of the KP tau-function is given. Namely, we prove that the CKP hierarchy can be identified with the restriction of odd times flows of the KP hierarchy on the locus of turning points of the second flow. The notion of CKP tau-function is clarified and connected with the KP tau function. Algebraic–geometrical solutions and in particular elliptic solutions are discussed in detail. A new identity for theta-functions of curves with holomorphic involution having fixed points is obtained.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-021-04119-6