主讲人：邓圣福

主讲人简介：邓圣福，华侨大学数学科学学院教授，福建省“闽江学者奖励计划”特聘教授，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、广东省“扬帆计划”引进紧缺拔尖人才项目等，并入选广东省高等学校“千百十人才培养工程”省级培养对象。在Archive for Rational Mechanics and Analysis、SIAM Journal on Mathematical Analysis、Nonlinearity、Journal of Differential Equations、Physica D.等国际重要学术期刊上发表论文40多篇。

报告内容概要：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.