# Events for 01/17/2023 from all calendars

## Nonlinear Partial Differential Equations

**Time: ** 3:00PM - 4:00PM

**Location: ** Zoom

**Speaker: **Abdon Moutinho, Université Paris 13

**Title: ***Dynamics of two interacting kinks for the phi6 model*

**Abstract: **We consider the $\phi^6$ model given by the one-dimensional nonlinear wave
equation $\partial_t^2 \phi - \partial_x^2 \phi + 2 \phi - 8 \phi^3 + 6 \phi^5 = 0$. In this talk, we will describe the long time behavior of all the solu-
tions of this partial differential equation satisfying the boundary condition
$\lim_{x \to \infty} \phi(t,x) = 1$, $\lim_{x \to -\infty} \phi(t,x) = -1$ and having energy slightly larger than the minimum possible. Indeed, we will also show that this set of solutions can be written explicitly as a sum of two moving kinks (topological solitons) with a remainder with low energy norm. Our estimate for the energy norm of the remainder is close to the optimal during the large time interval we study.