Seminar| Institute of Mathematical Sciences
Time: Friday, December 22th, 2023 , 14:30-15:30
Location：IMS, RS408
Speaker: Haitao Xu，Huazhong University of Science and Technology
Abstract: The study of localization phemomena has been a classic topic for centuries, which encourages the advance of theories for solitary waves and many others in nonlinear science. On the other hand, the recent developments in topological materials (such as topological insulators) provide various new examples and applications for linear localized states (e.g., edge states), which later are also extended to nonlinear settings. In this talk, we will give an introduction to linear and nonlinear edge states in lattices, with emphasis on the formation of edge states in finite-size lattices. Among lattice models with different dimensions and setups, we take a simple diatomic chain as a respresentative example to show how fintie-size effects are relevant to a typical formation mechanism for nonlinear localized states. Here the Large-Lattice limit is introduced to enable asymptotic analysis for eigenstates in linear lattices, which then plays a crucial role in estimating the emergence of nonlinear edge states. The discussed mechanism and analytical framework are expected to exist in a wider range of lattiece systems.
Abstract: The study of localization phemomena has been a classic topic for centuries, which encourages the advance of theories for solitary waves and many others in nonlinear science. On the other hand, the recent developments in topological materials (such as topological insulators) provide various new examples and applications for linear localized states (e.g., edge states), which later are also extended to nonlinear settings. In this talk, we will give an introduction to linear and nonlinear edge states in lattices, with emphasis on the formation of edge states in finite-size lattices. Among lattice models with different dimensions and setups, we take a simple diatomic chain as a respresentative example to show how fintie-size effects are relevant to a typical formation mechanism for nonlinear localized states. Here the Large-Lattice limit is introduced to enable asymptotic analysis for eigenstates in linear lattices, which then plays a crucial role in estimating the emergence of nonlinear edge states. The discussed mechanism and analytical framework are expected to exist in a wider range of lattiece systems.