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Browsing by Subject "soliton equations"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1
    (2006) Prikarpats'kìj, Ârema A.; Samojlenko, Anatolij Mihajlovič
    The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces are studied by means of differential-geometric and topological tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the construction presented we build pairs of Lax type commutative differential operator expressions related via a Delsarte-Darboux transformation and having a lot of applications in soliton theory.