KPII: Cauchy-Jost function, Darboux transformations and totally   nonnegative matrices
  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. 
M. Boiti (EINSTEIN Consortium, Lecce, Italy), F. Pempinelli (EINSTEIN   Consortium, Lecce, Italy), and A.K. Pogrebkov (Stekl...
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