Soliton dynamics for the generalized Choquard equation

We investigate the soliton dynamics for a class of nonlinear Schrödinger equations with a non-local nonlinear term. In particular, we consider what we call generalized Choquard equation   where the nonlinear term is (|x|θ−N⁎|u|p)|u|p−2u(|x|θ−N⁎|u|p)|u|p−2u. This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate.