  We investigate the soliton dynamics for a class of nonlinear Schr\"odinger
equations with a non-local nonlinear term. In particular, we consider what we
call {\em generalized Choquard equation} where the nonlinear term is
$(|x|^{\theta-N} * |u|^p)|u|^{p-2}u$. This problem is particularly interesting
because the ground state solutions are not known to be unique or
non-degenerate.
