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

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.

LaTeX, 24 pages

References in corpus (1)

• Cauchy--Jost function and hierarchy of integrable equations

Cited by in corpus (2)

• On soliton solutions and soliton interactions of Kulish-Sklyanin and Hirota-Ohta systems
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish