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

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

1998-10-31

arxiv.org/abs/cs/9811002v1

Computer Science

Symbolic Computation

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

Scientific paper

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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