The exotic conformal Galilei algebra and nonlinear partial differential equations |
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Authors: | Roman Cherniha Malte Henkel |
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Institution: | a Institute of Mathematics, National Academy of Science of Ukraine, 3, Tereshchenkivs'ka Str., UA-01601 Kyiv, Ukraine b Groupe de Physique Statistique, Département de Physique de la Matière et des Matériaux, Institut Jean Lamour,11Laboratoire associé au CNRS UMR 7198. CNRS - Nancy Université - UPVM, B.P. 70239, F-54506 Vandœuvre lès Nancy Cedex, France |
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Abstract: | The conformal Galilei algebra (cga) and the exotic conformal Galilei algebra (ecga) are applied to construct partial differential equations (PDEs) and systems of PDEs, which admit these algebras. We show that there are no single second-order PDEs invariant under the cga but systems of PDEs can admit this algebra. Moreover, a wide class of nonlinear PDEs exists, which are conditionally invariant under cga. It is further shown that there are systems of nonlinear PDEs admitting ecga with the realisation obtained very recently in D. Martelli, Y. Tachikawa, Comments on Galilei conformal field theories and their geometric realisation, preprint, arXiv:0903.5184v2 hep-th], 2009]. Moreover, wide classes of nonlinear systems, invariant under two different 10-dimensional subalgebras of ecga are explicitly constructed and an example with possible physical interpretation is presented. |
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Keywords: | Partial differential equation (PDE) Conformal Galilei algebra Lie symmetry Conditional symmetry |
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