Cauchy–Jost function and hierarchy of integrable equations

Theoretical and Mathematical Physics. 2015. Vol. 185. No. 2. P. 1599–1613.

Pogrebkov A., Boiti M., Pempinelli F.

We describe the properties of the Cauchy–Jost (also known as Cauchy–Baker–Akhiezer) function of the
Kadomtsev–Petviashvili-II equation. Using the ∂-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: обратная задача, inverse problem, Cauchy–Jost function, KP-II equation, функция Коши-Йоста, KP-II уравнение