学术报告:2018.5.23下午2:00-5:00,Dmitry Pelinovsky,McMaster University

发布时间:2018-05-14浏览次数:16

报告人:Dmitry Pelinovsky  

单位:McMaster University数学系

报告题目:Nonlinear PDEs on metric graphs

报告时间:2018年5月23日下午14:00-17:00地点数学学院第一报告厅

邀请人:陈金兵

报告摘要:I will give an overview of results for stationary states for the nonlinear Schr?dinger equation on different metric graphs, which include stars, tadpoles, dumbbell, and periodic graphs. For the subcritical power nonlinearity and for a star graph, a half-soliton state is a degenerate critical point of the action functional under the mass constraint such that the second variation is nonnegative. By using normal forms, we prove that the degenerate critical point is a saddle point, for which the small perturbations to the half-soliton state grow slowly in time resulting in the nonlinear instability of the half-soliton state. This phenomenon is just one example of a nontrivial interplay between the dynamical properties of the nonlinear PDEs and geometric properties of the metric graphs.

报告人简介Dmitry Pelinovsky 教授中文简介:

Dr. Dmitry Pelinovsky, McMaster University数学系教授,主要从事analysis of PDE, integrable systems and solitons, numerical computations等方向的研究,已在国际期刊:Communications in pure and applied Mathematics, SIAM Journal of Mathematical Analysis, Communications in Mathematical Physics, Communications in PDEs, Physics Reviewer Letters, Review in Mathematical Physics, AMS Contemporary Mathematics, Annales Henri Poincare, Inverse Problems, Nonlinearity, Studies in Applied Mathematics, Physica D等杂志发表200多篇SCI学术论文(H-index 34),并出版三本专著,1, Localization in Periodic potential; 2, Numerical Mathematics; 3, Nonlinear Physical System.目前还担任Studies in Applied Mathematics和Physica D编委,曾担任Physica Review A, Advance in Mathematical Physics 等多个期刊的编委。