Cauchy--Jost function and hierarchy of integrable equations
arXiv:1508.02229 · doi:10.1007/s11232-015-0367-y
Abstract
Properties of the Cauchy--Jost (known also as Cauchy--Baker--Akhiezer) function of the KPII equation are described. By means of the $\bar\partial$-problem for this function it is shown that all equations of the KPII hierarchy are given in a compact and explicit form, including equations on the Cauchy--Jost function itself, time evolutions of the Jost solutions and evolutions of the potential of the heat equation.