See also perturbative solution of the problem.
Here, the functions H and W depend on two variables, x and y.
H = H0 + H1 + H2, W = W0 + W1 + W2.
Harmonic parts are quadratic functions:
H0(x,y) = x2/2 + y2/2, W0(x,y) = wx2(x-x0)2/2 + wy2(y-y0)2/2.
We call wx and wy "frequencies", and x0 and y0 "displacements".
Download Mathematica programs used for this calculation
A paper related to minimizations of quadratic functions
Results of work at BGU with B. Segev
More on-line calculations