The natural extension to PDEs of Lie’s reduction of order algorithm for ODEs. arXiv:2407.09063
Preprint, arXiv:2407.09063 [math.AP] (2024).
Summary: In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural extension of Lie’s reduction of order algorithm for ordinary differential equations by looking at this algorithm from a different point of view. Many examples exhibit various situations that can arise.
MSC:
| 35A24 | Methods of ordinary differential equations applied to PDEs |
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 34C14 | Symmetries, invariants of ordinary differential equations |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
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