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arXiv · 1611.04198

KPII: Cauchy-Jost function, Darboux transformations and totally nonnegative matrices

M. Boiti·F. Pempinelli·A. K. Pogrebkov
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Abstract

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.

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M. Boiti, F. Pempinelli, A. K. Pogrebkov. 2016-11-13. KPII: Cauchy-Jost function, Darboux transformations and totally nonnegative matrices. https://doi.org/10.1088/1751-8121%2Faa7900

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