题目: Construction of multi solitary waves with symmetry for the nonlinear damped Klein–Gordon equation

报告人: 杜海铭 (BIMSA，清华大学)

时间：7月16日上午10点

地点：五教5206

摘要: We are interested in the nonlinear damped Klein-Gordon equation \[ \partial_t^2 u+2\alpha \partial_t u-\Delta u+u-|u|^{p-1}u=0 \] on $\RR^d$ for $2\le d\le 5$ and energy sub-critical exponents $2 < p < \frac{d+2}{d-2}$.

We construct multi-soliton, that is, solutions which behave for large times as a sum of decoupled solitons, in various configurations with symmetry:  this includes multi-soliton whose soliton centers lie at the vertices of an expanding regular polygon (with or without a center), of a regular polyhedron (with a center), of a higher dimensional regular polytope, or on a line. We give a precise description of these multi-solitons, in particular the interaction between nearest neighbour solitons is asymptotic to $\ln (t) - \frac{d-1}{2} \ln \ln t$ as $t \to +\infty$.

We also prove that in any multi-soliton, the solitons cannot share all the same sign.This a joint work with Raphaël Côte.