Nonlinear Wave Motion

非线性波动

• 批准号: 0070792
• 负责人: Mark Ablowitz
• 金额: $ 11.85万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-15 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070792&HistoricalAwards=false
• 关键词: Nonlinear; Wave; Motion

NSF Award Abstract - DMS-0070792Mathematical Sciences: Nonlinear Wave MotionAbstract0070792 AblowitzInvestigation of a new class of solutions to certain physically significant multidimensional nonlinear wave equations and associated linear scattering problems will continue. This work follows the discovery by the principal investigator that these solutions can be associated with an integer, referred to as the charge. Solutions and properties of a class of nonlinear differential-difference equations which arise in the study of fiber optic arrays will be obtained by employing analytical, computational and approximation/asymptotic techniques. Recent joint experimental-theoretical investigations of water waves by the principal investigator and collaborators has demonstrated that infinite dimensional chaotic dynamics can eventually result from the well known modulational instability of the classical Stokes water wave. The underlying mechanism governing this phenomenon has recently been uncovered. Further experiments and analysis are planned. Preliminary analysis has indicated that this dynamical scenario can also be observed in fiber optics.The dynamics of wave systems with large amplitude is often referred to as nonlinear wave motion. In contrast to the substantial theory available to understand small amplitude phenomena, the mathematical description of nonlinear wave motion is still in an early stage of development. Applications range from the study of large amplitude ocean waves to the propagation of pulses of light in fiber optics. Extremely stable, localized nonlinear waves, called solitons, are closely related to the investigations in this project. Solitons are being investigated worldwide due their potential use in high data rate communications over fiber-optic cables. The mathematical discoveries made in the field of nonlinear waves only a few years ago are now at the cusp of commercial

美国国家科学基金会奖摘要- DMS-0070792数学科学：非线性波运动摘要0070792 Ablowitz调查一类新的解决方案，某些物理上重要的多维非线性波方程和相关的线性散射问题将继续。 这项工作遵循主要研究者的发现，这些解决方案可以与一个整数相关联，称为电荷。 利用解析、计算和近似/渐近技术，得到了光纤阵列研究中出现的一类非线性微分-差分方程的解及其性质。 最近由主要研究者和合作者对水波进行的联合实验-理论研究表明，无穷维混沌动力学最终可能源于经典斯托克斯水波的众所周知的调制不稳定性。 这种现象的内在机制最近被揭示出来。 计划进行进一步的实验和分析。 初步分析表明，这种动力学现象也可以在光纤中观察到，具有大振幅的波动系统的动力学通常被称为非线性波动。 与理解小振幅现象的大量理论相反，非线性波动的数学描述仍处于发展的早期阶段。 应用范围从大振幅海浪的研究到光纤中光脉冲的传播。 非常稳定的局域非线性波，称为孤子，与本项目的研究密切相关。 由于孤子在光纤电缆上的高数据速率通信中的潜在用途，孤子正在世界范围内被研究。 仅仅几年前在非线性波领域的数学发现现在正处于商业化的风口浪尖