Mini-Workshop: Attraction to Solitary Waves and Related Aspects of Physics

Abstract

The aim of the miniworkshop is the discussion of the solitary wave asymptotics for nonlinear Hamiltonian partial differential equations and relation to mathematical problems of Quantum Physics. While the existence and orbital stability of solitary waves is fairly well understood, the asymptotic stability of solitary waves is still not understood well. The global attraction of arbitrary solutions of finite energy to the set of solitary waves is not proved but in a few model cases. On the other side, there is now accumulating a great number of recent results that seem to enable us to make a crucial progress in this direction: namely, to prove the solitary asymptotics for the U(1)-invariant nonlinear Klein-Gordon equation and similar dispersive Hamiltonian systems. On the Quantum Physics side, the workshop contained the thorough discussion of the quantum scattering and renormalization analysis