Solutions of the relativistic nonlinear wave equation by solutions of the nonlinear Schrِdinger equation

Using an ansatz for nonlinear complex wave equations obtained by using Lie point symmetries, we show how to construct new solutions of the relativistic nonlinear wave equation from those of a nonlinear Schrِdinger equation with the same nonlinearity. This ansatz reduces the number of space-time variables by one, and is not related to a contraction. We give some examples of other types of hyperbolic equations admitting solutions based on nonlinear Schrِdinger equations.