Geodesic
Cauchy--Jost function and hierarchy of integrable equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 272-288

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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, inverse problem.
Mots-clés : KP-II equation 
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     title = {Cauchy--Jost function and hierarchy of integrable equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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M. Boiti; F. Pempinelli; A. K. Pogrebkov. Cauchy--Jost function and hierarchy of integrable equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 272-288. http://geodesic.mathdoc.fr/item/TMF_2015_185_2_a2/