The exotic conformal Galilei algebra and nonlinear partial differential equations

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 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 ECGA are explicitly constructed and an example with possible physical interpretation is presented.

Latex2e, 18 pages, no figures; final version, J. Math. Anal. Appl. at press

References in corpus (2)

• On nonlinear partial differential equations with an infinite-dimensional conditional symmetry
• On the dynamical symmetric algebra of ageing: Lie structure, representations and Appell systems

Cited by in corpus (32)

• Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
• Galilean Conformal Mechanics from Nonlinear Realizations
• Dynamical realization of l-conformal Galilei algebra and oscillators
• Nonrelativistic conformal groups and their dynamical realizations
• On dynamical realizations of l-conformal Galilei groups
• Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations
• Dynamical realizations of N=1 l-conformal Galilei superalgebra
• N=2 supersymmetric extension of l-conformal Galilei algebra
• Dynamical symmetries and causality in non-equilibrium phase transitions
• On logarithmic extensions of local scale-invariance
• On non-local representations of the ageing algebra
• Schrödinger symmetry: a historical review
• Logarithmic Correlators in Non-relativistic Conformal Field Theory
• Supersymmetry of the planar Dirac - Deser-Jackiw-Templeton system, and of its non-relativistic limit
• Causality from dynamical symmetry: an example from local scale-invariance
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• $\ell$-oscillators from second-order invariant PDEs of the centrally extended Conformal Galilei Algebras
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Unitary representations of N-conformal Galilei group
• Remark on higher-derivative mechanics with l-conformal Galilei symmetry
• Non-local representations of the ageing algebra in higher dimensions
• Logarithmic Exotic Conformal Galilean Algebras
• Physical ageing and new representations of some Lie algebras of local scale-invariance
• Galilean conformal algebras in two spatial dimension
• Invariant PDEs with Two-dimensional Exotic Centrally Extended Conformal Galilei Symmetry
• Logarithmic correlators or responses in non-relativistic analogues of conformal invariance
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• The Shigesada-Kawasaki-Teramoto model: conditional symmetries, exact solutions and their properties
• Galilean Conformal Algebra in Semi-Infinite Space
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• Nonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows. II: The two-dimensional space case
• Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension