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Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs

We construct, for any given $ \ell = \frac{1}{2} + {\mathbb N}_0, $ the second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. The generators are obtained by a coset construction and the PDEs are constructed by standard Lie symmetry technique. It is observed that the invariant PDEs have significant difference for $ \ell > \frac{3}{2}. $

preprint2015arXivOpen access
Naruhiko AizawaTadanori Kato
math-phmath.MP
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Naruhiko AizawaTadanori Kato

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