
Symmetry and Integrability of Equations of Mathematical Physics − 2018
Vasyl Fedorchuk (Institute of MAthematics, Pedagogical University, Cracow, Poland and Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine,
Lviv, Ukraine)
Volodymyr Fedorchuk (Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine,
Lviv, Ukraine)
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 lowdimensional ($\dim L \le3$) 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
threedimensional 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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[17] Fedorchuk V.M. and Fedorchuk V.I., Classification of Symmetry Reductions for the Eikonal Equation, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine, Lviv, 2018. 176 pp.

