The partition function of the extended \({r}\)-reduced Kadomtsev-Petviashvili hierarchy. (English) Zbl 1317.37067
Summary: We derive a particular solution of the extended \({r}\)-reduced KP hierarchy, which is specified by a generalized string equation . The work is a generalization to arbitrary \(r\geqslant 2\) of Buryak’s recent results of a solution to the extended open KdV hierarchy which corresponds to \({r} = 2\).
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
| 53D45 | Gromov-Witten invariants, quantum cohomology, Frobenius manifolds |
