Reduction and Some Exact Solutions of the Eikonal Equation

Using the nonsplitting subgroups of the generalized Poincareg roupP (1, 4), ansatzes which reduce the eikonal equation to differential equations with a lesser number of independent variables are constructed. The corresponding symmetry reduction is made. Some classes of exact solutions of the investigated equation are presented. The relativistic eikonal (the relativistic Hamilton-Jacobi) equation is fundamental in the- oretical and mathematical physics. We consider the equation ∂u ∂xµ ∂u ∂x µ ≡ ∂u ∂x0 2 − ∂u ∂x1 2 − ∂u