Centrally extended conformal Galilei algebras and invariant nonlinear PDEs (Q2406257)

Summary: We construct, for any given \(\ell=\frac{1}{2}+\mathbb N_0\), second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the algebras obtained by coset construction and we employ the standard Lie point symmetry technique for the construction of PDEs. It is observed that the invariant PDEs have significant difference for \(\ell>\frac{3}{2}\).