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.
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Sections 3, 4, and 5 were written by A. K. Pogrebkov, and Secs. 1, 2, and 6 were written by M. Boiti and F. Pempinelli.
The research of A. K. Pogrebkov was funded by a grant from the Russian Science Foundation (Project No. 14- 50-00005) and was performed at the Steklov Mathematical Institute of the Russian Academy of Sciences.
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 185, No. 2, pp. 272–288, November, 2015.
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Boiti, M., Pempinelli, F. & Pogrebkov, A.K. Cauchy–Jost function and hierarchy of integrable equations. Theor Math Phys 185, 1599–1613 (2015). https://doi.org/10.1007/s11232-015-0367-y
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DOI: https://doi.org/10.1007/s11232-015-0367-y