TY - JOUR
ID - Prykarpatsky2006
LB - Prykarpatsky2006
AU - Prykarpatsky, Yarema A.
AU - Samoilenko, Anatoliy M.
TI - The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1
ST - The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1
JO - Opuscula Math.
JA - Opuscula Math.
JF - Opuscula Mathematica
PY - 2006
VL - 26
IS - 1
SP - 137
EP - 150
UR - http://www.opuscula.agh.edu.pl/vol26/1/art/opuscula_math_2610.pdf
AB - 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.
KW - Delsarte transmutation operators
KW - parametric functional spaces
KW - Darboux transformations
KW - inverse spectral transform problem
KW - soliton equations
KW - Zakharov-Shabat equations
SN - 1232-9274
ER -