Formal solutions to the KP hierarchy
Sergey Mironovich Natanzon, Anton Vladimirovich Zabrodin · Journal of Physics A Mathematical and Theoretical · 2016
We find all formal solutions to the ℏ-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.