Lie Symmetries and Criticality of Semilinear Differential Systems
Mathematical Physics
2008-04-24 v1 Analysis of PDEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.
Keywords
Cite
@article{arxiv.math-ph/0703071,
title = {Lie Symmetries and Criticality of Semilinear Differential Systems},
author = {Yuri Bozhkov and Enzo Mitidieri},
journal= {arXiv preprint arXiv:math-ph/0703071},
year = {2008}
}
Comments
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/