English

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

Symbolic Computation 2007-05-23 v1 Exactly Solvable and Integrable Systems solv-int

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.

Keywords

Cite

@article{arxiv.cs/9811002,
  title  = {Factorization of linear partial differential operators and Darboux integrability of nonlinear PDEs},
  author = {Serguei P. Tsarev},
  journal= {arXiv preprint arXiv:cs/9811002},
  year   = {2007}
}

Comments

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