动力系统中的不变流形理论专题报告II

主讲人：孙春友教授/邓圣福教授 兰州大学/华侨大学

时间：2022年11月5日14:30

地点：腾讯会议 233 479 353

举办单位：数理学院

主讲人介绍：孙春友，兰州大学教授，博士生导师。1999年在云南大学数学系本科毕业，2005年在兰州大学数学与统计学院获基础数学博士学位。主要从事非线性分析和无穷维动力系统的研究，特别是无穷维动力系统吸引子的存在性、维数估计、吸引速度估计、渐近正则性、有限维降维、时空复杂性等。截止目前，发表学术论文40余篇，多篇论文发表在研究领域的主要期刊上，如 Mathematische Annalen, Transaction Amer. Math. Soc.,SIAM J. Math. Anal., SIAM J. Applied Dynamical Systems, J. Differential Equations,Proceedings Royal Society Edinburgh, J. Evolutionary Equations, Nonlinearity等。 邓圣福, 华侨大学教授，从事微分方程与动力系统理论及其在水波问题上的应用。先后主持国家自然科学面上基金3项、教育部留学回国人员科研启动基金、中国博士后科学基金、福建省自然科学基金、广东省自然科学基金。在Arch. Rational Mech. Anal.、SIAM J. Math. Anal.、Nonlinearity、J. Differential Equations、Physica D等国际重要学术期刊上发表论文40多篇。

内容介绍：

孙春友教授报告摘要：We will report our recent results about the existence of an inertial manifold for a 3D complex Ginzburg-Landau equation with periodic boundary conditions. This is a joint work with Dr. Anna Kostianko and professor Sergey Zelik. 

邓圣福教授报告摘要：This talk considers the existence of one- or two-hump solutions of a singularly perturbed nonlinear Schrödinger (NLS) equation, which is the standard NLS equation with a third order perturbation. In particular, this equation appears in the field of nonlinear optics, where it is used to describe pulses in optical fibers near a zero dispersion wavelength. It has been shown formally and numerically that the perturbed NLS equation has one- or multi-hump solutions with small oscillations at infinity, called generalized one- or multi-hump solutions. The main purpose here is to provide the first rigorous proof of the existence of generalized one- or two-hump solutions of the singularly perturbed NLS equation. The several invariant properties of the equation, i.e., the translational invariance, the gauge invariance and the reversibility property, are essential to obtain enough free constants to prove the existence. The ideas and methods presented here may be applicable to show existence of generalized 2^k-hump solutions of the equation.