On Some Applications of the Nonconjugate Subgroups of the Generalized Poincare Group P(1,4)
V.M.Fedorchuk (Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of NAS of Ukraine, Lviv, Ukraine); V.I.Fedorchuk (Franko Lviv National University, Lviv, Ukraine.)
The subgroup structure of the generalized Poincare group P(1,4) has been studied. For all nonconjugate subgroups of the group P(1,4), the functional bases of the invariants in the five-dimensional Minkowski space M(1,4) have been constructed. The results obtained have been used in order to solve the next task: - the symmetry reduction and construction of exact solutions for some linear and nonlinear differential equations in the spaces M(1,4)xR(u) and M(1,3)xR(u). In the space M(1,4)xR(u), we considered the nonlinear wave equation and the Dirac equation. In the space M(1,3)xR(u), we investigated the eikonal equation, the multidimensional Euler-Lagrange-Born-Infeld equation, the multidimensional homogeneous and inhomogeneous Monge-Ampere equations; - the description of the systems of coordinates in the space M(1,4) in which the linear wave equation admits partial or full separation of variables; - the construction of differential equations of the first-order in the spaces M(1,4)xR(u) and M(1,3)xR(u) which are invariant under splitting subgroups of the group P(1,4).
Section : 12