Scattering in the nonlinear Lamb system

We obtain long time asymptotics for the solutions to a string coupled to a nonlinear oscillator: each finite energy solution decays to a sum of a stationary state and a dispersive wave. The asymptotics hold in global energy norm. The dispersive waves are expressed via initial data and solution to an ordinary differential equation. The asymptotics give a mathematical model for the Bohr's transitions between quantum stationary states.