Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs

TL;DR

This paper constructs second-order nonlinear PDEs invariant under centrally extended conformal Galilei algebras for specific parameter values, revealing notable differences in the equations' structure for higher parameter values.

Contribution

It introduces a systematic method to derive invariant nonlinear PDEs for all half-integer values of , using coset construction and Lie symmetry techniques.

Findings

Invariant PDEs differ significantly for  > 3/2

Constructs PDEs for all  = 1/2 + N0

Uses coset and Lie symmetry methods

Abstract

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}. $