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Moving Frames for Laplace Invariants

Shemyakova, Ekaterina and Mansfield, Elizabeth L. (2008) Moving Frames for Laplace Invariants. In: Jeffrey, D., ed. ISSAC '08 Proceedings of the twenty-first international symposium on Symbolic and algebraic computation. ISSAC International Symposium on Symbolic and Algebraic Computation . ACM, New York, USA, pp. 291-298. ISBN 978-1-60560-494-7. (doi:10.1145/1390768.1390809) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1145/1390768.1390809

Abstract

The development of symbolic methods for the factorization and integration of linear PDEs, many of the methods being generalizations of the Laplace transformations method, requires the finding of complete generating sets of invariants for the corresponding linear operators and their systems with respect to the gauge transformations \(L -> g(x,y)-^1 O\) \(L\) \(O\) \(g(x,y)^{-1}\). Within the theory of Laplace-like methods, there is no uniform approach to this problem, though some individual invariants for hyperbolic bivariate operators, and complete generating sets of invariants for second- and third-order hyperbolic bivariate ones have been obtained. Here we demonstrate a systematic and much more efficient approach to the same problem by application of moving-frame methods. We give explicit formulae for complete generating sets of invariants for second- and third-order bivariate linear operators, hyperbolic and non-hyperbolic, and also demonstrate the approach for pairs of operators appearing in Darboux transformations.

Item Type: Book section
DOI/Identification number: 10.1145/1390768.1390809
Uncontrolled keywords: Symbolic computations ; Algebraic computations
Subjects: Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Elizabeth Mansfield
Date Deposited: 10 May 2010 14:07 UTC
Last Modified: 03 Oct 2019 15:14 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/23874 (The current URI for this page, for reference purposes)
Mansfield, Elizabeth L.: https://orcid.org/0000-0002-6778-2241
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