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Formal solution to the $\hbar-$KP hierarchy

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Speaker: 
Sergey Natanzon
Affiliation: 
HSE Moscow/MPIM
Date: 
Tue, 2018-07-24 14:00 - 15:00
Location: 
MPIM Lecture Hall

We find all formal solutions to the $\hbar$-dependent Kadomtsev-Petviashvili (KP) hierarchies. For $\hbar=1$ and $\hbar=0$ they are solutions of standard KP hierarchy and dispersionless KP hierarchy respectively. The solutions are characterized by certain Cauchy-like data that are functions of one variable. The solutions are found in a form of formal series for the tau-functions of the hierarchies and for its logarithms. An explicit combinatorial description of the coefficients of the series is provided. The talk is based on join work with A.Zabrodin.
 

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