Fedorchuk V. Group classification of non-linear five-dimensional D'Alembert equations and first-order differential invariants of non-conjugate subgroups of the Poincare group P(1,4)

In the thesis a group classification of a certain class of non-linear five-dimensional D'Alembert equations in the space M(1,4)xR(u) has been performed. Non-equivalent functional bases of the first-order differential invariants for non-conjugate subgoups of the Poincare group P(1,4) have been constructed. A criterion of equivalence for functional bases of the first-order differential invariants for non-conjugate subgoups of the Poincare group P(1,4) has been formulated and proven. For some P(1,4)-invariant five-dimensional D'Alembert equations, the symmetry reduction has been performed and some classes of invariant solutions have been constructed.