Constructive factorization of LPDO in two variables

Details Constructive factorization of LPDO in two variables Constructive factorization of LPDO in two variables

2005-04-06

arxiv.org/abs/math-ph/0504019v1

TMPh (Journal of Theoretical and Mathematical Physics) 145(2), pp. 1510-1523. (2005)

Physics

Mathematical Physics

16 pages, to be published in Journal "Theor. Math. Phys." (2005)

Scientific paper

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.

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