DIVISION OF DIFFERENTIAL OPERATORS, INTERTWINE RELATIONS AND DARBOUX TRANSFORMATIONS

The problem of a differential operator left- and right division is Asolved in terms of generalized Bell polynomials for a nonabelian Adifferential unitary ring. The definition of the polynomials is made Aby means of recurrent relations. The expressions of classic Bell Apolynomials via a generalized one is given. Conditions of exact factorization lead to intertwine relations and result in linearizable Ageneralized Burgers equation. An alternative proof of the Matveev Atheorem is given and transformation formulae for the coefficients of Adifferential operator in terms of differential polynomials follow from Athe intertwine relation.