In this talk we will consider the small data regime of a quadratic Klein-Gordon equation in 3D. Motivated by the question of asymptotic stability of coherent structures (such as solitons) in dispersive equations, the results presented will focus on the long-time behavior of solutions.

The main new feature in the problem we study is the presence of an internal mode. This brings new challenges, such as both anomalously slow decay (worse than linear) and poor spatial localization of the field.

This is joint work with Fabio Pusateri.

Zoom link: https://princeton.zoom.us/j/92147928280