Localised modes in discrete lattices

离散晶格中的局域模式

• 批准号: EP/D069513/1
• 负责人: Robert MacKay
• 金额: $ 2.55万
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD069513%2F1
• 关键词: Localised; modes; discrete; lattices

Interplay between nonlinearity and periodicity is the focus of recent studies in different branches of modern applied mathematics and nonlinear physics. Our research program is in mathematical analysis of discrete dynamical systems. We aim to study nonlinear models expressed by the differential advanced-delay equations, difference equations and partial differential equations in the context of applications to photonic band-gap engineering, nonlinear optics, and atomic physics of Bose-Einstein condensates. The research program consists of several specific goals (problems): (1) derivation of the discrete nonlinear Schrodinger equation and the coupled-mode (Dirac) system, (2) persistence of traveling waves in discrete lattices, and (3) bifurcations and stability of three-dimensional discrete vortices.

非线性与周期性之间的相互作用是现代应用数学和非线性物理各分支的研究热点。我们的研究项目是离散动力系统的数学分析。我们的目标是研究由微分超前延迟方程，差分方程和偏微分方程表示的非线性模型的应用背景下，光子带隙工程，非线性光学，玻色-爱因斯坦凝聚体的原子物理。研究计划包括几个具体的目标（问题）：（1）离散非线性薛定谔方程和耦合模（Dirac）系统的推导，（2）离散格子中行波的持续性，（3）三维离散涡的分叉和稳定性。

项目成果

Justification of the Lattice Equation for a Nonlinear Elliptic Problem with a Periodic Potential

具有周期势的非线性椭圆问题格方程的证明

• DOI: 10.1007/s00220-008-0640-0
• 发表时间: 2008
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Pelinovsky D