Formal solution to the KP hierarchy
classification
🧮 math-ph
hep-thmath.MPnlin.SI
keywords
formalhierarchyseriessolutionscauchy-likecertaincharacterizedcoefficients
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We find all formal solutions to the $\hbar$-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.
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