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)