Wave trains in a 2D diatomic face-centered lattice

讲座时间 Datetime: 2022年9月12日，星期一，10:00-11:00

地点 Venue: 腾讯会议：434-145-642

主持人 Host：唐德

报告人 Speaker: 郭上江  

单位 Affiliation: 中国地质大学（武汉）

报告摘要 Abstract:

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.