Abstract |

**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.)*

*e-mail:
vas_fedorchuk@yahoo.com*

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