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Theoretical and Mathematical Physics

, Volume 185, Issue 2, pp 1599–1613 | Cite as

Cauchy–Jost function and hierarchy of integrable equations

  • M. Boiti
  • F. Pempinelli
  • A. K. Pogrebkov
Article

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 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.EINSTEIN ConsortiumLecceItaly
  2. 2.Steklov Mathematical Institute of the Russian Academy of SciencesMoscowRussia

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