On the Classification of Symmetry Reductions and Invariant Solutions for the Euler–Lagrange–Born–Infeld Equation
Keywords:structural properties of Lie argebras, nonsingular manifolds, classification of symmetry reductions, invariant solutions, Poincar´e group P(1, 4), Euler–Lagrange–Born–Infeld equation
We study a connection between the structural properties of the low-dimension (dimL ≤ 3) nonconjugate subalgebras of the Lie argebra of the generalized Poincar´e 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.
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