Formal solutions to the KP hierarchy. (English) Zbl 1346.37055

Natanzon, S. M.; Zabrodin, A. V.

J. Phys. A, Math. Theor. 49, No. 14, Article ID 145206, 20 p. (2016).

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.

Reviewer: Vladislav Nikolaevich Dumachev (Voronezh)

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