Ivan Franko National University of Lviv,
1 Universytetska Street, Lviv, 79000, UKRAINE
E-mail: matmod@franko.lviv.ua

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.


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