Formal solution to the KP hierarchy

Abstract

We find all formal solutions to the $\hslash$-dependent KP hierarchy. They are characterized by certain Cauchy-like data. The solutions are found in the form of formal series for the tau-function of the hierarchy and for its logarithm (the F-function). An explicit combinatorial description of the coefficients of the series is provided.

23 pages, no figures

References in corpus (1)

• Laplacian growth in a channel and Hurwitz numbers

Cited by in corpus (3)

• Kadomtsev-Petviashvili turning points and CKP hierarchy
• Kadomtsev-Petviashvili hierarchies of types B and C
• On the Expansion Coefficients of Tau-function of the BKP Hierarchy