Obstacles to the Factorization of Linear Partial Differential Operators into Several Factors

Abstract

We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations. We derive some interesting facts about the new objects, for instance, that they are invariant under gauge transformations. An important theorem for the construction of factoring algorithms is proved: a factorization is defined uniquely from a certain moment on. For operators of orders three and two, obstacles are found explicitly.

References in corpus (1)

• Hierarchy of general invariants for bivariate LPDOs

Cited by in corpus (4)

• Multiple Factorizations of Bivariate Linear Partial Differential Operators
• Laplace maps and constraints for a class of third order partial differential operators
• Parametric Factorizations of Second-, Third- and Fourth-Order Linear Partial Differential Operators with a Completely Factorable Symbol on the Plane
• Refinement of Two-Factor Factorizations of a Linear Partial Differential Operator of Arbitrary Order and Dimension