Factorization in categories of systems of linear partial differential equations

Details Factorization in categories of systems of linear partial differential equations Factorization in categories of systems of linear partial differential equations

2008-01-09

arxiv.org/abs/0801.1341v1

Computer Science

Symbolic Computation

LaTeX, 23 pages

Scientific paper

We start with elementary algebraic theory of factorization of linear ordinary differential equations developed in the period 1880-1930. After exposing these classical results we sketch more sophisticated algorithmic approaches developed in the last 20 years. The main part of this paper is devoted to modern generalizations of the notion of factorization to the case of systems of linear partial differential equations and their relation with explicit solvability of nonlinear partial differential equations based on some constructions from the theory of abelian categories.

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