Factorization of linear partial differential operators and Darboux integrability of nonlinear PDEs
<|reference_start|>Factorization of linear partial differential operators and Darboux integrability of nonlinear PDEs: 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.<|reference_end|>
@article{tsarev1998factorization,
    title={Factorization of linear partial differential operators and Darboux
  integrability of nonlinear PDEs},
    author={Serguei P. Tsarev},
    journal={arXiv preprint arXiv:cs/9811002},
    year={1998},
    archivePrefix={arXiv},
    eprint={cs/9811002},
    primaryClass={cs.SC nlin.SI solv-int}
}