  Using the two-dimensional nonlinear Schr\"odinger equation (NLS) as a model
example, we present a general method for recovering the nonlinearity of a
nonlinear dispersive equation from its small-data scattering behavior. We prove
that under very mild assumptions on the nonlinearity, the wave operator
uniquely determines the nonlinearity, as does the scattering map. Evaluating
the scattering map on well-chosen initial data, we reduce the problem to an
inverse convolution problem, which we solve by means of an application of the
Beurling--Lax Theorem.
