  We present a general algorithm to show that a scattering operator associated
to a semilinear dispersive equation is real analytic, and to compute the
coefficients of its Taylor series at any point. We illustrate this method in
the case of the Schrodinger equation with power-like nonlinearity or with
Hartree type nonlinearity, and in the case of the wave and Klein-Gordon
equations with power nonlinearity. Finally, we discuss the link of this
approach with inverse scattering, and with complete integrability.
