This article is cited in 3 papers

Cauchy–Jost function and hierarchy of integrable equations

M. Boiti^a, F. Pempinelli^a, A. K. Pogrebkov<sup>b

a</sup> EINSTEIN Consortium, Lecce, Italy
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We describe the properties of the Cauchy–Jost (also known as Cauchy–Baker–Akhiezer) function of the Kadomtsev–Petviashvili-II equation. Using the $\bar\partial$-method, we show that for this function, all equations of the Kadomtsev–Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy–Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.

Keywords: Cauchy–Jost function, KP-II equation, inverse problem.

Received: 30.04.2015

DOI: 10.4213/tmf8982

 English version: Theoretical and Mathematical Physics, 2015, 185:2, 1599–1613

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