This article is cited in 8 papers

Constructively Factoring Linear Partial Differential Operators in Two Variables

R. Beals^a, E. A. Kartashova<sup>b

a</sup> Yale University
^b Johannes Kepler University Linz

Abstract: We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or an ordinary linear differential operator admits a factorization with a first-order factor on the left.The process of factoring consists of recursively solving systems of linear equations subject to certain differential compatibility conditions.In the general case of partial differential operators, it is not necessary to solve a differential equation. In special degenerate cases, such as an ordinary differential operator, the problem eventually reduces to solving some Riccati equation(s). We give the factorization conditions explicitly for the second and third orders and in outline form for higher orders.

Keywords: differential operators, factorization of differential operators, algebraic factorization.

Received: 28.01.2005

DOI: 10.4213/tmf1892

 English version: Theoretical and Mathematical Physics, 2005, 145:2, 1511–1524

Bibliographic databases:

• 
• 
• 
• 
•