@book{b7ee83f2ff38452ca0dd2fcef3cabbef,

title = "Elementary Darboux transformations for the $n$-component $KP$-hierarchy",

abstract = "In this paper a purely algebraic setting is described in which a characterization of the dual wavefunctions of the multicomponent $KP$-hierarchy and an interpretation of the bilinear form of this system of nonlinear equations can be given. The framework enables the construction of solutions starting from a matrix version of the Sato Grassmannian and the expression in formal power series determinants, the so-called $\tau$-functions. This leads to a geometric description of the elementary Darboux transformations for the $n$-component $KP$-hierarchy and one concludes with showing how to construct them, both at the differential operator level as at the $\tau$-function level.",

keywords = "METIS-208643, MSC-22E65, MSC-35Q58, EWI-3465, MSC-58B25, IR-65831, MSC-22E70",

author = "G.F. Helminck and {van de Leur}, J.W. and {van de Leur}, J.W.",

note = "Imported from MEMORANDA",

year = "2002",

language = "Undefined",

series = "Memorandum Faculty Mathematical Sciences",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1645",

}