报告地点：Zoom会议 ID：822 9883 5431 密码：295123
邀请人：高洪俊教授&郭飞教授
报告摘要：Breathers are temporally periodic and spatially localized solutions ofevolutionary PDEs. They are known to exist for integrable PDEs such as the sine-Gordon equation, but are believed to be rare for general nonlinear PDEs. When thespatial dimension is equal to one, exchanging the roles of time and space variables (inthe so-called spatial dynamics framework), breathers can be interpreted as homoclinicsolutions to steady solutions and thus arising from the intersections of the stable andunstable manifolds of the steady states. In this talk, we shall study small breathers ofthe nonlinear Klein-Gordon equation generated in an unfolding bifurcation as a pair ofeigenvalues collide at the original when a parameter (temporal frequency) varies. Due tothe presence of the oscillatory modes, generally the finite dimensional stable andunstable manifolds do not intersect in the infinite dimensional phase space, but with anexponentially small splitting (relative to the amplitude of the breather) in this singularperturbation problem of multiple time scales. This splitting leads to the transversalintersection of the center-stable and center-unstable manifolds which produces smallamplitude generalized breathers with exponentially small tails. Due to the exponentialsmall splitting, classical perturbative techniques cannot be applied. We will explain howto obtain an asymptotic formula for the distance between the stable and unstablemanifold of the steady solutions. This is a joint work with O. Gomide, M. Guardia, and T.Seara.
报告人简介：曾崇纯。美国佐治亚理工学院教授。研究方向为应用动力系统与非线性偏微分方程，美国杨百翰大学博士毕业，主持多想美国国家自然科学基金，2004年获斯隆奖（Sloan Fellowship），2019年入选美国数学学会会士（AMS Fellow）。他在国际顶尖数学期刊《Invent. Math.》《Comm. Pure Appl. Math》《Mem. Am. Math. Soc.》等发表论文30余篇。
