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Foundations of Computational Mathematics

, Volume 8, Issue 4, pp 501–532 | Cite as

Algorithms for Differential Invariants of Symmetry Groups of Differential Equations

Article

Abstract

We develop new computational algorithms, based on the method of equivariant moving frames, for classifying the differential invariants of Lie symmetry pseudo-groups of differential equations and analyzing the structure of the induced differential invariant algebra. The Korteweg-deVries (KdV) and Kadomtsev-Petviashvili (KP) equations serve to illustrate examples. In particular, we deduce the first complete classification of the differential invariants and their syzygies of the KP symmetry pseudo-group.

Keywords

Symmetry Group Recurrence Formula Determine Equation Moving Frame Differential Invariant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Society for the Foundations of Computational Mathematics 2006

Authors and Affiliations

  1. 1.Department of Mathematics, University of St. ThomasSt. Paul, MN 55105USA
  2. 2.School of Mathematics, University of MinnesotaMinneapolis, MN 55455USA
  3. 3.Department of Mathematics, Oregon State UniversityCorvallis, OR 97331USA

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