Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The exotic conformal Galilei algebra and nonlinear partial differential
  equations   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.

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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
1
The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con