Volume 19, Issue 2, June 2012, Pages 158 - 181
Lie Theorem via Rank 2 Distributions (Integration of PDE of Class ω = 1)
Authors
Boris Kruglikov
Institute Mathematics and Statistics, NT-Faculty, University of Tromsø, Tromsø 90-37, Norway,boris.kruglikov@uit.no
Received 24 August 2011, Accepted 21 December 2011, Available Online 4 July 2012.
- DOI
- 10.1142/S1402925112500118How to use a DOI?
- Keywords
- Lie's class 1; Darboux integrability; system of PDEs; characteristic; integral; Goursat flag; symbols; compatibility; Spencer cohomology
- Abstract
In this paper we investigate compatible overdetermined systems of PDEs on the plane with one common characteristic. Lie's theorem states that its integration is equivalent to a system of ODEs, and we give a new proof by relating it to the geometry of rank 2 distributions. We find a criterion for integration in quadratures and in closed form, and discuss nonlinear Laplace transformations and symmetric PDE models.
- Copyright
- © 2012 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Boris Kruglikov PY - 2012 DA - 2012/07/04 TI - Lie Theorem via Rank 2 Distributions (Integration of PDE of Class ω = 1) JO - Journal of Nonlinear Mathematical Physics SP - 158 EP - 181 VL - 19 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925112500118 DO - 10.1142/S1402925112500118 ID - Kruglikov2012 ER -