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

NSF奖摘要-DMS-0070792数学科学：非线性波动运动摘要0070792 Ablowitz对某些具有物理意义的多维非线性波动方程及其相关线性散射问题的一类新解的研究将继续进行。这项工作是在首席研究员发现这些解可以与一个被称为电荷的整数相关联之后进行的。利用解析、计算和逼近/渐近技术，得到了光纤阵列研究中出现的一类非线性微分-差分方程组的解和性质。最近，主要研究人员和合作者对水波的联合实验和理论研究表明，无限维混沌动力学最终可能是众所周知的经典Stokes水波调制不稳定性的结果。支配这种现象的潜在机制最近被揭开了。计划进行进一步的实验和分析。初步分析表明，这种动力学场景也可以在光纤中观察到。大振幅波动系统的动力学通常被称为非线性波动。与可用于理解小振幅现象的大量理论相比，非线性波动的数学描述仍处于早期发展阶段。应用范围从研究大幅度海浪到光脉冲在光纤中的传播。极稳定的局域非线性波，称为孤子，与该项目的研究密切相关。由于孤子在光缆上的高数据率通信中的潜在用途，全世界都在研究孤子。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尖端。