Algorithms for differential invariants of symmetry groups of differential equations

Jeongoo Cheh, Peter J. Olver, Juha Pohjanpelto

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)501-532
Number of pages32
JournalFoundations of Computational Mathematics
Volume8
Issue number4
DOIs
StatePublished - Aug 1 2008

Keywords

  • Differential equation
  • Differential invariant
  • Kadomtsev-Petviashvili equation
  • Korteweg-de Vries equation
  • Lie pseudo-group
  • Moving frame
  • Symmetry group

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