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Formal solution to the KP hierarchy

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arxiv 1509.04472 v1 pith:YV6OO3F6 submitted 2015-09-15 math-ph hep-thmath.MPnlin.SI

S. Natanzon , A. Zabrodin This is my paper · ORCID
classification math-phhep-thmath.MPnlin.SI
keywords formalhierarchyseriessolutionscauchy-likecertaincharacterizedcoefficients
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

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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  1. Integrable hierarchies with zero dispersion and elliptic curves

    nlin.SI 2026-05 unverdicted novelty 6.0 of 10

    Dispersionless limits of KP, Toda, and Pfaff-type hierarchies possess a dynamical algebraic curve (genus 0 or 1) that can be uniformized by rational, trigonometric, or elliptic functions.

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