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We study a connection between the structural properties of the low-dimension (dimL ≤ 3) nonconjugate subalgebras of the Lie argebra of the generalized Poincaré group P (1,4) and the results of symmetry reductions for the Euler–Lagrange–Born–Infeld equation. We have performed the classification of nonsingular manifolds in the space M (1 , 3 ) × R(u) invariant with respect to three-dimensional nonconjugate subalgebras of the Lie algebra of the group P (1,4). The results are used for the classification of symmetry reductions and invariant solutions of the Euler–Lagrange–Born–Infeld equation.

On the Classification of Symmetry Reductions and Invariant Solutions for the Euler–Lagrange–Born–Infeld Equation