Mild-slope Equation - Transformation To An Inhomogeneous Helmholtz Equation

Transformation To An Inhomogeneous Helmholtz Equation

Through the transformation

the mild slope equation can be cast in the form of an inhomogeneous Helmholtz equation:

\Delta\psi\, +\, k_c^2\, \psi\, =\, 0 \qquad \text{with} \qquad k_c^2\, =\, k^2\, -\, \frac{\Delta\left(\sqrt{c_p\,c_g}\right)}{\sqrt{c_p\,c_g}},

where is the Laplace operator.

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