  We show that, for the 1d cubic NLS equation, widely separated equal amplitude
in-phase solitons attract and opposite-phase solitons repel. Our result gives
an exact description of the evolution of the two solitons valid until the
solitons have moved a distance comparable to the logarithm of the initial
separation. Our method does not use the inverse scattering theory and should be
applicable to nonintegrable equations with local nonlinearities that support
solitons with exponentially decaying tails. The result is presented as a
special case of a general framework which also addresses, for example, the
dynamics of single solitons subject to external forces.
