Yuriy
SYDORENKO
Ivan Franko National University of Lviv,
1 Universytetska Street, Lviv, 79000, UKRAINE
Email: matmod@franko.lviv.ua
Factorization of differential operators, Darboux transformations
and integration of constrained KP and mKP hierarchies
Abstract:
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
KadomtsevPetviashvili (cKP) and modified KadomtsevPetviashvili (cmKP)
hierarchies is given as applications.
References:

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Sidorenko Yu. Binary transformation and (2+1)dimensional integrable systems,
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Sidorenko Yu. Transformation operators for integrable hierarchies with
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Part 1. (2002) 352357.

Sidorenko Yu.M., Berkela Yu.Yu. Integration of nonlinear spacetwodimensional
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Sidorenko Yu.M. Factorization of matrix differential operators and Darbouxlike
transformations, Mat. Studii, 19, No.2. (2003), to be published.