Nonlinear Geometrical Optics

Linear geometrical optics
describe the propagation of
waves with high frequency as
the propagations of rays and
supplies an approximate
solution. The approximate
solution is considerably
easier to evaluate
numerically, than the
actual solution to the
partial differential
equation. For nonlinear
phenomena there exists a
number of studies and
heuristics, while the
development of a stringent
theory is still only
commencing. For instance,
the exponential functions
in the linear approximation
need to be replaced by more
general 'profiles' in order
to take the creation of
harmonics into account.