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Extending the analysis to 2D (and 3D)
u(x,y,t) = g(k_xx + k_yy - \omega t)
is a typically solution of
u_{tt} = c^2(u_{xx} + u_{yy})
Can build solutions by adding complex Fourier components
of the form
e^{i(k_xx + k_yy - \omega t)}
