Evolution of localized modes in nonlinear dispersive equations

非线性色散方程中局域模态的演化

• 批准号: 238931-2011
• 负责人: Pelinovsky, Dmitry
• 金额: $ 1.89万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508804
• 关键词: Evolution; localized; modes; nonlinear; dispersive

Nonlinear dispersive equations include partial differential equations for wave propagation and differential-difference equations for excitation dynamics in lattices. The proposed research will be focused on the fundamental and applied problems related to the nonlinear wave propagation in the periodic inhomogeneous media such as granular crystals, optical cavity resonators, and the dielectric materials with low-frequency dispersion. The novelty and significant differences of the underlying models from classical Korteweg-De Vries and nonlinear Schrodinger equations make the topics fascinating for researchers in applied analysis of dynamical systems.

非线性色散方程包括波传播的偏微分方程和晶格中激发动力学的微分差分方程。本论文的主要研究方向是非线性波在周期性非均匀介质中的传播，如颗粒晶体、光学谐振腔和低频色散介质材料。它与经典的Korteweg-De弗里斯方程和非线性薛定谔方程的新奇和显著差异，使其成为动力系统应用分析研究的热点。