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## Formal solutions to the KP hierarchy

Journal of Physics A: Mathematical and Theoretical. 2016. Vol. 49. No. 14. P. 22.

We find all formal solutions to the -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.