  We study localized solutions for the nonlinear graph wave equation on finite
arbitrary networks. Assuming a large amplitude localized initial condition on
one node of the graph, we approximate its evolution by the Duffing equation.
The rest of the network satisfies a linear system forced by the excited node.
This approximation is validated by reducing the nonlinear graph wave equation
to the discrete nonlinear Schrodinger equation and by Fourier analysis.
Finally, we examine numerically the condition for localization in the parameter
plane, coupling versus amplitude and show that the localization amplitude
depends on the maximal normal eigenfrequency.

Pattern Formation and Solitons