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 Schrodinger 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 Schrodinger equations.

Published in 2004

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