Lie Symmetries and Criticality of Semilinear Differential Systems

Details Lie Symmetries and Criticality of Semilinear Differential Systems Lie Symmetries and Criticality of Semilinear Differential Systems

2007-03-25

arxiv.org/abs/math-ph/0703071v1

SIGMA 3 (2007), 053, 17 pages

Physics

Mathematical Physics

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2007.053

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.

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