perturbation technique to compute surface wave stokes solutions

Dear Maxima users,

I am working on oceanic surface waves and I would like to compute the
well-known Stokes solution to this problem at various orders. The
first order solution, which is also know as Airy's wave, is obtained
from irrotational potential flow theory providing that the surface
undulation is given (as a harmonic function). Solutions at higher
order are obtained with a asymptotic/expansion technique.

I am quite unexperienced to softwares allowing symbolic calculus and I
would like to know if it is possible to use the method of expansions
in Maxima. If so, could you please give some directions?

Thank you very much by advance,

C?dric Ody