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Formal solutions to the KP hierarchy. (English) Zbl 1346.37055
Authors’ abstract: We find all formal solutions to the $$\hslash$$-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.

##### MSC:
 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
##### Keywords:
integrable hierarchies; tau-function; Hirota equation
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