  According to the Alday-Maldacena program the strong coupling limit of Super
Yang-Mills scattering amplitudes is given by minimal area surfaces in AdS
spacetime with a boundary consisting of a momentum space polygon. The string
equations in AdS systematically reduce to coupled Toda type equations whose
Euclidean classical solutions are then of direct relevance. While in the
simplest case of AdS_3 exact solutions were known from earlier studies of the
sinh-Gordon equation, there exist at present no similar exact forms for the
generalized Toda equations related to AdS_d with d>=4. In this paper we develop
a series method for the solution to those equations and evaluate their
contribution to the finite piece of the worldsheet area. For the known
sinh-Gordon case the method is seen to give results in excellent agreement with
the exact answer.
