Kadomtsev-Petviashvili turning points and CKP hierarchy

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.

arXiv comment44 pages, no figures

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Cited by in corpus (11)

• CKP hierarchy and free Bosons
• Toda lattice with constraint of type B
• Constrained Toda hierarchy and turning points of the Ruijsenaars-Schneider model
• Kadomtsev-Petviashvili hierarchies of types B and C
• The generalized Giambelli formula and polynomial KP and CKP tau-functions
• Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations
• Tau functions, infinite Grassmannians and lattice recurrences
• Elliptic families of solutions to constrained Toda hierarchy
• Monodromy free linear equations and many-body systems
• Novikov-Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model
• Characterizing Jacobians of algebraic curves with involution