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Factorization of linear partial differential operators and Darboux integrability of nonlinear PDEs

Serguei P. Tsarev
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Abstract

Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems of the Loewy-Ore theory of factorization of linear ordinary differential operators. Possible applications to factorized Groebner bases computations in the commutative and non-commutative cases are discussed, an application to finding criterions of Darboux integrability of nonlinear PDEs is given.

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BibTeXRIS

Serguei P. Tsarev. 1998-10-31. Factorization of linear partial differential operators and Darboux integrability of nonlinear PDEs. https://arxiv.org/abs/cs/9811002

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