Ivan Franko National University of Lviv,
1 Universytetska Street, Lviv, 79000, UKRAINE
Factorization of differential operators, Darboux transformations
and integration of constrained KP and mKP hierarchies
A factorization of a matrix differential operator of general form into
elementary factors is constructed in explicit form. A notion of simplest
elementary Darboux transformations is introduced. The theory of general
Darboux type transformations for matrix evolutionary differential operators
of arbitrary order is developed. Binary Darboux type transformations for
such operators are also constructively represented. Integration of constrained
Kadomtsev-Petviashvili (cKP) and modified Kadomtsev-Petviashvili (cmKP)
hierarchies is given as applications.
Samoilenko A.M., Samoilenko V.G., Sidorenko Yu.M. Hierarchy of the Kadomtsev-Petviashvili
equations under nonlocal constraints: Many-dimensional generalizations
and exact solutions of reduced systems, Ukr. Math. Journ.
Sidorenko Yu. Binary transformation and (2+1)-dimensional integrable systems,
Ukr. Math. Journ. 54, No.11. (2002) 1531-1550.
Sidorenko Yu. Transformation operators for integrable hierarchies with
additional reductions, Proceedings of Institute of Math. of NAS of Ukraine.
Part 1. (2002) 352-357.
Sidorenko Yu.M., Berkela Yu.Yu. Integration of nonlinear space-twodimensional
Heisenberg equations, Mat. Studii, 18, No.1. (2002) 57-68.
Sidorenko Yu.M. Factorization of matrix differential operators and Darboux-like
transformations, Mat. Studii, 19, No.2. (2003), to be published.