  Direct definition of the Cauchy-Jost (known also as Cauchy-Baker-Akhiezer)
function in the case of pure solitonic solution is given and properties of this
function are discussed in detail using the Kadomtsev-Petviashvili II equation
as example. This enables formulation of the Darboux transformations in terms of
the Cauchy-Jost function and classification of these transformations. Action of
Darboux transformations on Grassmanians-i.e., on the space of soliton
parameters-is derived and relation of the Darboux transformations with property
of total nonnegativity of elements of corresponding Grassmanians is discussed.
