On symmetry reduction of the Euler-Lagrange-Born-Infeld equation to linear ODEs

Abstract

Connections between structure properties of three-dimensional subalgebras of the Poincare algebra ${\mathfrak p}(1,4)$ and Lie reductions of the Euler-Lagrange-Born-Infeld equation are studied. We concentrate our attention on Lie reductions with respect to three-dimensional subalgebras that reduce the Euler-Lagrange-Born-Infeld equation to linear ordinary differential equations.