Articles dans des revues à comité de lecture
|The exotic conformal Galilei algebra and non-linear partial differential equations|
|Cherniha R., Henkel M.|
|J. Math. Anal. Appl. 369 (2010) 120|
|DOI : doi:10.1016/j.jmaa.2010.02.025|
|ArXiv : arxiv:0910.4822 [PDF]|
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 non-linear PDEs admitting ECGA with the realisation obtained very recently in [D. Martelli and Y. Tachikawa, arXiv:0903.5184v2 [hep-th] (2009)]. Moreover, wide classes of non-linear systems, invariant under two different 10-dimensional subalgebras of the ECGA are explicitly constructed and an example with a possible physical interpretation is presented.