Natanzon, S. M.; Zabrodin, A. V. Formal solutions to the KP hierarchy. (English) Zbl 1346.37055 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) Cited in 1 ReviewCited in 2 Documents 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 PDF BibTeX XML Cite \textit{S. M. Natanzon} and \textit{A. V. Zabrodin}, J. Phys. A, Math. Theor. 49, No. 14, Article ID 145206, 20 p. (2016; Zbl 1346.37055) Full Text: DOI