Speaker: 张笑然，BIMSA

Inviter: 范晨捷 副研究员

Title: A review of Soffer-Weinstein's proof of instability in Hamiltonian, resonant nonlinear wave equations

Language: Chinese

Time & Venue: 2024.12.20  16:00-17:00  S813

Abstract: We will give a review of Soffer, Weinstein's work[Invent. math. 1999]. They consider a class of nonlinear Klein-Gordon equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. They showed that, for generic nonlinear Hamiltonian perturbations, all small amplitude solutions decay to zero as time tends to infinity at an anomalously slow rate, because of the resonance. In particular, spatially localized and time-periodic solutions of the linear problem are destroyed by generic nonlinear Hamiltonian perturbations via slow radiation of energy to infinity.