# Template:Green's function equations for the diffracted potential

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We use the Free-Surface Green Function for two-dimensional waves, with singularity at the water surface since we are only interested in its value at $\displaystyle{ z=0 }$ (details about this method can be found in Integral Equation for the Finite Depth Green Function at Surface). Using this we can transform the system of equations to
$\displaystyle{ \phi^{\mathrm{D}}(x) = \phi^{\mathrm{I}}(x) + \int_{-L}^{L}G(x,\xi) \alpha\phi^{\mathrm{D}}(\xi) \mathrm{d} \xi }$