报告题目：Existence of generalized solitary wave solutions for a diatomic

Fermi-Pasta-Ulam-Tsingou

报告人： 邓圣福（华侨大学）

报告时间：2023年12月8日（星期五）上午9:00-10:00

报告地点：东六C座507会议室

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。

摘要：This talk concerns the existence of generalized solitary wave solutions (solitary wave solutions exponentially tending to small periodic solutions) for a diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. This existence has been proved by Faver and Wright (SIAM J. Math. Anal., 50 (2018), 182-250) with a  functional analytic technique. We give the same result by a different approach---dynamical system method. The FPUT lattice is formulated as a  dynamical system under the traveling wave frame. Then the center manifold reduction theorem with the Laurent expansion is applied to show that this system can be reduced to a system of ordinary differential equations with dimension 5. Its dominant system has a homoclinic solution. Using a perturbation method and adjusting some appropriate constants, we prove that this homoclinic solution persists for the whole ordinary differential system, which is connected to a periodic solution with algebraically small amplitude (called generalized homoclinic solution, thereafter). This yields the existence of a generalized solitary wave solution for the FPUT lattice.

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2023.12.04