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

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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.
LaTeX 2.09, acmconf.sty (included in the tar file), 8 pages. Presented at the Poster session of ISSAC'98 (Rostock, Germany)

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Symbolic Computation, Exactly Solvable and Integrable Systems, I.1

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http://salesiana.dossiersoluciones.com/handle/123456789/33075

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cs/9811002
 http://arxiv.org/abs/cs/9811002

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arXiv