Laplace invariants of differential operators
Mathematical Physics
2020-12-22 v3 math.MP
Abstract
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential invariants of partial differential operators under gauge transformations and introduce a sufficient condition for a set of invariants to be complete. We also give a some mild conditions that guarantee the existence of such a set. The proof is constructive. The method gives many examples of invariants previously known in the literature as well as many new examples including multidimensional.
Cite
@article{arxiv.2003.03467,
title = {Laplace invariants of differential operators},
author = {David Hobby and Ekaterina Shemyakova},
journal= {arXiv preprint arXiv:2003.03467},
year = {2020}
}