Cauchy–Jost function and hierarchy of integrable equations
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.