Classical scattering in (1 + 1)-dimensional string theory

We find the general solution to Polchinski's classical scattering equations for (1 + 1)-dimensional string theory. This allows efficient computation of scattering amplitudes in the standard Liouville×c=1 background. Moreover, the solution leads to a mapping from a large class of time-dependent collective field theory backgrounds to corresponding nonlinear σ models. Finally, we derive recursion relations between tachyon amplitudes. These may be summarized by an infinite set of nonlinear partial differential equations for the partition function in an arbitrary time-dependent background.