Effective Threshold Dynamics for the Cubic Nonlinear Klein–Gordon Equation in Three Dimensions

In the last two decades a remarkable surge of results in dispersive PDE have addressed qualitative features of the dynamics of large solutions, based on methods such as the Kenig-Merle approach. On the other hand, effective quantitative results appear to be almost unavailable. In this talk I will present recent work with Jaime Gomez, giving an effective quantitative estimate of scattering solutions near the scattering threshold for the cubic nonlinear Klein-Gordon equation, as described by Nakanishi-Schlag. The main ingredient is an induction on energy type argument, but in the context of a focussing nonlinear wave equation.