Abstract: We consider the nonlinear Hartree equation in (1+4) dimensions and obtain multisoliton solutions for which the trajectories are approximated to leading order by an N-body law. The proof is based on an adapted approximation scheme going back to Krieger-Martel-Raphaël for a two-soliton and Wu for a multisoliton solution in the 3D Hartree equation. By symmetry we obtain finite-time collision blow up at the pseudo-conformal rate, for which we can prescribe distinct collision points and multiplicity of soliton mass at each point. The talk is based on joint work with J.Gòmez (EPFL) and Y. Wu (Yale) as well as a follow-up paper with Y. Wu.
