Journal of Nonlinear Mathematical Physics

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Volume 18, Issue 4, December 2011, Pages 583 - 611

Laplace Transformation of Lie Class ω = 1 Overdetermined Systems

Authors
Boris Kruglikov
Institute of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway,boris.kruglikov@uit.no
Received 19 April 2011, Accepted 20 August 2011, Available Online 7 January 2021.
DOI
10.1142/S1402925111001805How to use a DOI?
Keywords
Lie's class 1; overdetermined systems of PDEs; characteristic; integral; symbols; compatibility; Spencer cohomology
Abstract

In this paper, we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on one function of one variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal theory of PDEs.

Copyright
© 2011 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
18 - 4
Pages
583 - 611
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925111001805How to use a DOI?
Copyright
© 2011 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

risenwbib
TY  - JOUR
AU  - Boris Kruglikov
PY  - 2021
DA  - 2021/01/07
TI  - Laplace Transformation of Lie Class ω = 1 Overdetermined Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 583
EP  - 611
VL  - 18
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001805
DO  - 10.1142/S1402925111001805
ID  - Kruglikov2021
ER  -