Group Analysis of Differential Equations and Integrable Systems − 2018

Sergey Natanzon (National Research University Higher School of Economics, Moscow, Russia)

Formal solution to the $\hbar-$KP hierarchy

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

The talk is based on join work with A. Zabrodin.