Division of Differential operators, intertwine relations and Darboux Transformations
Abstract
The problem of a differential operator left and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The expresions of classic Bell polinomils via generalized one is given. The conditions of an exact factorization possibility leads to the intertwine relation and results in some linearizable generalized Burgers equation. An alternative proof of the Matveev theorem is given and Darboux  Matveev transformations formula for coefficients follows from the intertwine relations and also expressed in the generalized Bell polinomials.
 Publication:

arXiv eprints
 Pub Date:
 March 1999
 arXiv:
 arXiv:mathph/9903005
 Bibcode:
 1999math.ph...3005L
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics