報告人：鄧聖福 (華僑大學)

報告題目：Two-Hump Traveling-Wave Solutions of a Diatomic Fermi-Pasta-Ulam-Tsingou Lattice

報告摘要：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.

報告時間：2024年12月4日（星期三）10:00-11:30

報告地點：騰訊會議：575-611-484

邀請人：李骥

報告人簡介：鄧聖福, 華僑大學教授，福建省“閩江學者獎勵計劃”特聘教授，從事微分方程與動力系統理論及其在水波問題上的應用。先後主持國家自然科學面上基金3項、教育部留學回國人員科研啟動基金、中國博士後科學基金、福建省自然科學基金、廣東省自然科學基金、廣東省“揚帆計劃”引進緊缺拔尖人才項目等，曾入選廣東省高等學校“千百十人才培養工程”省級培養對象。在Arch. Rational Mech. Anal.、SIAM J. Math. Anal.、Nonlinearity、J. Differential Equations、Physica D等國際重要學術期刊上發表論文40多篇。