Kadomtsev-Petviashvili turning points and CKP hierarchy

TL;DR

This paper characterizes the CKP hierarchy within the KP framework, linking tau-functions and algebraic-geometrical solutions, including elliptic solutions, and introduces new identities for theta-functions of symmetric curves.

Contribution

It provides a novel characterization of the CKP hierarchy via KP tau-functions and explores algebraic-geometrical solutions, including elliptic solutions, with new theta-function identities.

Findings

CKP hierarchy identified as restriction of KP odd flows on turning points

Clarification of CKP tau-function and its relation to KP tau function

Derivation of new theta-function identities for symmetric curves

Abstract

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. The new identity for theta-functions of curves with holomorphic involution having fixed points is obtained.