Elena Kartaschova, R. Beals,
"Constructively factoring linear partial differential operators in two variables"
, in Journal of Theoretical and Mathematical Physics, Vol. 145, Nummer 2, Springer Science+Business Media, Seite(n) 1510-1523, 11-2005, ISSN: 0040-5779
Constructively factoring linear partial differential operators in two variables
Sprache des Titels:
We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process consists of solving, recursively, systems of linear equations, subject to certain differential compatibility conditions. In the generic case of partial differential operators one does not have to solve a differential equation. In special degenerate cases, such as ordinary differential, the problem is finally reduced to the solution of some Riccati equation(s). The conditions of factorization are given explicitly for second- and, and an outline is given for the higher-order case.