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

  • V. M. Fedorchuk Institute of Mathematics, Pedagogical University, Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine
  • V. I. Fedorchuk Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine
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

Abstract

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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Published
2019-12-09
How to Cite
Fedorchuk, V., & Fedorchuk, V. (2019). On the Classification of Symmetry Reductions and Invariant Solutions for the Euler–Lagrange–Born–Infeld Equation. Ukrainian Journal of Physics, 64(12), 1103. https://doi.org/10.15407/ujpe64.12.1103
Section
Fields and elementary particles