Laplace invariants of differential operators

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.

References in corpus (7)

• Proof of the Completeness of Darboux Wronskian Formulae for Order Two
• Classification of Multidimensional Darboux Transformations: First Order and Continued Type
• Differential operators on the superline, Berezinians, and Darboux transformations
• Invertible Darboux Transformations
• Laplace maps and constraints for a class of third order partial differential operators
• Differential operators on the algebra of densities and factorization of the generalized Sturm-Liouville operator
• Factorization of Darboux-Laplace transformations for discrete hyperbolic operatros