报告摘要：In this talk, we investigate the existence and branching patterns of wave trains  in a 2D face-centered square  lattice consisting of alternating light and heavy atoms, with linear coupling between  nearest particles and a nonlinear  substrate potential. In contrast to monatomic chains, we consider two different periodic waveform functions corresponding to light  and heavy particles, respectively. As a result, we have to solve coupled advanced-delay differential equations, which are reduced to a finite-dimensional bifurcation equation with an inherited Hamiltonian structure by applying a Lyapunov-Schmidt reduction. Then we obtain the small-amplitude solutions in the Hamiltonian system near equilibria in non-resonance and p:q resonance, respectively. In particular, the results can be applied to some one-dimensional diatomic lattices. This is a joint work with Dr Ling Zhang at CUG.

个人简介：郭上江，中国地质大学(武汉)二级教授、博士生导师、数理学院院长，湖南大学岳麓学者特聘A岗教授、博士生导师。主要从事微分方程分岔理论及应用研究，随机动力系统理论及应用研究。主持国家自然科学基金项目6项，在Springer出版社应用数学科学丛书出版了英文专著一部，在JDE、JNLS、M3AS、DCDS和Nonlinearity等杂志上发表论文80多篇。2014-2019及2021年入选“中国高被引学者”榜单。获湖南省自然科学奖一等奖(排名第一，2018年)、湖南省科技进步一等奖(排名第二，2008年)。担任包含国际SCI刊物《Bulletin of the Malaysian Mathematical Sciences Society》在内的4个学术刊物的编委。