报告题目：One- and two-hump solutions of a singularly perturbed cubic nonlinear Schrödinger equation
时 间：2023-04-15 (星期六) 15:30 ~ 2023-04-15 (星期六) 16:30
地 点：理工南楼618
主 办：数学与统计学院, 福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
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.
报告人简介：邓圣福，华侨大学教授，“闽江学者奖励计划”特聘教授，主要研究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基金面上项目3项、福建省和广东省自然科学基金多项，曾入选广东省“扬帆计划”引进紧缺拔尖人才、广东省高等学校“千百十人才培养工程”省级培养对象等。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。