邓圣福：Two-Hump Traveling-Wave Solutions of a Diatomic Fermi-Pasta-Ulam-Tsingou Lattice

报告承办单位: 数学与统计学院

报告内容: The talk concerns the traveling-wave solutions for a diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. It has been shown that such a lattice has a generalized solitary-wave solution exponentially approaching a periodic solution with algebraically small amplitude at infinity. We give a rigorous proof of the existence of two-hump solutions for a diatomic FPUT lattice using a dynamical system method together with the center manifold reduction theorem obtained from the Laurent series expansion of the resolvent operator for the linear part of the problem. The distance of these two humps is large and the two humps are connected by algebraically small oscillations in between. The main idea of the proof is to find two appropriate free constants such that two one-hump solutions can be successfully stuck together in the middle to form a two-hump solution. The idea here may also be used to study the existence of 2^k-hump solutions.

报告人姓名: 邓圣福

报告人所在单位: 华侨大学

报告人职称/职务及学术头衔: 教授

报告时间: 2025年6月18日下午14:00-18:00

报告地点:云塘校区理科楼A212

报告人简介:邓圣福, 华侨大学教授，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，曾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。