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Theoretical and Mathematical Physics

, Volume 145, Issue 2, pp 1511–1524 | Cite as

Constructively Factoring Linear Partial Differential Operators in Two Variables

  • R. Beals
  • E. A. Kartashova
Article

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 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • R. Beals
    • 1
  • E. A. Kartashova
    • 2
  1. 1.Yale UniversityNew HavenUSA
  2. 2.Johannes Kepler Universitat (JKU) LinzLinzAustria

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