Asymptotic stability of the sine-Gordon kink outside symmetry
数学专题报告
报告题目(Title)：Asymptotic stability of the sine-Gordon kink outside symmetry
报告人(Speaker)：Prof. Gong Chen (Georg. Inst. Tech., USA)
地点(Place)：腾讯会议（会议号: 889 907 783，密码：683689）
时间(Time)：2025年10月17日（周五）9:00-10:00
邀请人(Inviter)：徐桂香
报告摘要
We consider scalar field theories on the line with Ginzburg-Landau (double-well) self-interaction potentials. Prime examples include the \phi^4 model and the sine-Gordon model. These models feature simple examples of topological solitons called kinks. The study of their asymptotic stability leads to a rich class of problems owing to the combination of weak dispersion in one space dimension, low power nonlinearities, and intriguing spectral features of the linearized operators such as threshold resonances or internal modes.
We present a perturbation proof of the full asymptotic stability of the sine-Gordon kink outside symmetry under small perturbations in weighted Sobolev norms. The strategy of our proof combines a space-time resonances approach based on the distorted Fourier transform to capture modified scattering effects with modulation techniques to take into account the invariance under Lorentz transformations and under spatial translations. A major difficulty is the slow local decay of the radiation term caused by the threshold resonances of the non-selfadjoint linearized matrix operator around the modulated kink. Our analysis hinges on two remarkable null structures that we uncover in the quadratic nonlinearities of the evolution equation for the radiation term as well as of the modulation equations. The entire framework of our proof, including the systematic development of the distorted Fourier theory, is general and not specific to the sine-Gordon model.
主讲人简介
Gong Chen is an assistant professor in mathematics at Georgia Institute of Technology， USA. Gong Chen got his PhD from the University of Chicago in 2017. He did his postdoc at the University of Toronto. He jointed Georgia Institute of Technology in 2022.
