Invariant operators of four-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4)

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

“…More precisely, we have presented only the results of the symmetry reduction for those types of three-dimensional nonconjugate subalgebras of the Lie algebra of the group (1, 4) which give reductions to identities. It is known [19] that the Lie algebra of the group (1, 4) contains three-dimensional nonconjugate subalgebras of the following types: 3 1 , 2 ⊕ 1 , 3.1 , 3.2 , 3.3 , 3.4 , 3.6 , 3.7 , 3.8 , and 3.9 . From the results obtained, it follows that all above-presented symmetry reductions of the Euler-Lagrange-Born-Infeld equation to identities can be obtained using some subalgebras of the following types: 3 1 , 3.1 , 3.6 .…”

“…Let us consider the Euler-Lagrange-Born-Infeld equation of the form (1, 4). As we wrote earlier, the results of the classification of all the low-dimensional (dim ≤ 3) nonconjugate subalgebras of the Lie algebra of the group (1, 4) can be found in [19].…”

“…The classification of all nonconjugate subalgebras of the Lie algebra of the group (1, 4) of dimensions ≤3 was performed in [19].…”

On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation

“…It follows from that paper that the Lie algebra of the symmetry group of the equation under consideration contains, as subalgebra, the Lie algebra of the group P (1, 4). As we mentioned before, the results of the classification of all the low-dimensional (dim L ď 3) nonconjugate subalgebras of the Lie algebra of the group P (1, 4) could be found in [8]. We will present below some of the results obtained.…”

“…The classification of all nonconjugate subalgebras of the Lie algebra of the group P (1, 4) of dimensions ď 3 was performed in [8].…”