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 − 2 u . This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate.