Marco Ghimenti (University of Pisa)
Title: Soliton dynamics for the generalized Choquard equation

Abstract: We study the soliton dynamics for a class of nonlinear Schrodinger equations with a non-local nonlinear term. We prove that soliton solutions under the effect of an external potential exhibit in the semi-classical limit a particle-like behavior. We consider what we call generalized Choquard equation and we give a description of the soliton dynamics.
A similar result exist for standard Choquard equation but the proof relies on the non degeneracy of ground states which is not known for the generalized Choquard equation. This problem can be avoided when the nonlinear effect is sufficiently strong, and we developed a method that in this case provide a description of soliton dynamics.