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Texas A&M University

Events for 01/17/2023 from all calendars

Nonlinear Partial Differential Equations

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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.