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 language | English (US) |
|---|---|
| Pages (from-to) | 501-532 |
| Number of pages | 32 |
| Journal | Foundations of Computational Mathematics |
| Volume | 8 |
| Issue number | 4 |
| DOIs | |
| State | Published - Aug 2008 |
Keywords
- Differential equation
- Differential invariant
- Kadomtsev-Petviashvili equation
- Korteweg-de Vries equation
- Lie pseudo-group
- Moving frame
- Symmetry group