Journal of Nonlinear Mathematical Physics

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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
19 - 2
Pages
158 - 181
Publication Date
2012/07/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925112500118How to use a DOI?
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  -