On classification of symmetry reductions for the Euler–Lagrange–Born–Infeld equation

Abstract:
It is well known, that the symmetry reduction is one of the most powerful tools for investigation of partial differential equations.
We study a connection between structural properties of low-dimensional ($\dim L \le3$) nonconjugate subalgebras of the Lie argebra of the generalized Poincaré group $P(1,4)$ and results of symmetry reduction for the Euler–Lagrange–Born–Infeld equation.
We plan to present some results concerning the relationship between the classification of three-dimensional nonconjugate subalgebras of the Lie algebra of the group $P(1,4)$ and types of reduced equations for the Euler–Lagrange–Born–Infeld equation.

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