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Collaborative Research: Collapse, Rogue Waves, and their Applications: From Theory to Computation and Beyond

合作研究：塌陷、异常波浪及其应用：从理论到计算及其他

基本信息

批准号：
2204702
负责人：
Panayotis Kevrekidis
金额：
$ 21.93万
依托单位：
University of Massachusetts Amherst
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2204702&HistoricalAwards=false
关键词：
Collaborative Research Collapse Rogue Waves

项目摘要

The project aims to further the understanding of collapse-type phenomena and rogue waves in systems that are modeled by nonlinear ordinary, partial, and lattice differential equations. Collapse-type phenomena are mathematically described by solutions that remain self-similar as some of their attributes become unbounded in finite time. Self-similarity refers to preservation of shape when an appropriate scaling of space and time and solution amplitude is employed. Collapse phenomena are relevant to the focusing of light beams in optics and to atomic matter waves. Rogue waves have a characteristic length or time scale and extreme amplitudes; they are important in subjects such as hydrodynamics, nonlinear optics, and atomic and plasma physics. Using dynamical systems and computational techniques, this project aims to reformulate the underlying models and provide a unified approach to studying both collapse phenomena and rogue waves by treating the relevant patterns as self-similar solutions. The project is expected to provide insights on the mechanisms and reduced mathematical descriptions of collapse phenomena in some of the prototypical mathematical models that feature these potentially catastrophic focusing events, as well as on the formation, prediction, and analysis of extreme waves in both continuum and spatially discrete systems. The project will offer research training opportunities for students. The project will explore a recently derived normal form for the study of self-focusing waves of the central dispersive wave model of the nonlinear Schrödinger equation and will seek generalizations for related models (such as the Korteweg-de Vries equation). Stability analysis of such collapsing waves is expected to shed light on the spectral properties and potential instabilities of such systems, their connection to symmetries, their implications for the dynamics in different settings (supercritical, critical, and subcritical), and their reinterpretation in the original "non-exploding'' frame. A second focus of the project will be the study of rogue waves from a dynamical systems viewpoint, including characterization of stability via limits of time-periodic solutions and rogue waves in higher-order dispersion settings. The theoretical analysis will be corroborated by numerical simulations involving deflation-based fixed-point techniques and pseudo-arclength continuation, as well as state-of-the-art contour integral-based eigenvalue solvers. Collaboration with experimental groups performing laboratory experiments will also be sought.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目旨在进一步了解由非线性常微分方程、偏微分方程和格点微分方程建模的系统中的湍流型现象和流氓波。崩溃型现象在数学上是由解描述的，这些解在有限时间内保持自相似，因为它们的一些属性变得无界。自相似性是指当采用适当的空间和时间缩放以及解振幅时形状的保持。坍缩现象与光学中光束的聚焦和原子物质波有关。无规则波具有特征长度或时间尺度和极端振幅;它们在流体力学、非线性光学、原子和等离子体物理等学科中很重要。利用动力系统和计算技术，该项目旨在重新制定基础模型，并通过将相关模式视为自相似解决方案，提供一种统一的方法来研究崩溃现象和流氓波。该项目预计将提供的机制和减少的数学描述的崩溃现象的一些原型的数学模型，功能这些潜在的灾难性的聚焦事件，以及在连续和空间离散系统的极端波的形成，预测和分析的见解。该项目将为学生提供研究培训机会。该项目将探讨最近导出的标准形式，用于研究非线性薛定谔方程中心色散波模型的自聚焦波，并将寻求相关模型（如Korteweg-de弗里斯方程）的推广。这种坍缩波的稳定性分析有望揭示这种系统的光谱特性和潜在的不稳定性，它们与对称性的联系，它们对不同环境（超临界，临界和亚临界）中动力学的影响，以及它们在原始“非爆炸”框架中的重新解释。该项目的第二个重点将是从动力系统的角度研究流氓波，包括通过时间周期解的限制和高阶色散设置中的流氓波来表征稳定性。理论分析将得到证实的数值模拟，涉及放气为基础的定点技术和伪弧长延续，以及国家的最先进的轮廓积分为基础的本征值求解器。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（15）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Control of Dy164 Bose-Einstein condensate phases and dynamics with dipolar anisotropy

DOI：
10.1103/physrevresearch.4.043124
发表时间：
2022-05
期刊：
Physical Review Research
影响因子：
4.2
作者：
S. Halder;K. Mukherjee;S. Mistakidis;S. Das;P. Kevrekidis;P. Panigrahi;Soumya Majumder;H. Sadeghpour
通讯作者：
S. Halder;K. Mukherjee;S. Mistakidis;S. Das;P. Kevrekidis;P. Panigrahi;Soumya Majumder;H. Sadeghpour

How close are integrable and nonintegrable models: A parametric case study based on the Salerno model

可积模型和不可积模型有多接近：基于萨莱诺模型的参数化案例研究

DOI：
10.1103/physreve.107.024202
发表时间：
2023
期刊：
Physical Review E
影响因子：
2.4
作者：
Mithun, Thudiyangal;Maluckov, Aleksandra;Mančić, Ana;Khare, Avinash;Kevrekidis, Panayotis G.
通讯作者：
Kevrekidis, Panayotis G.

An Ising machine based on networks of subharmonic electrical resonators

基于分谐波电谐振器网络的伊辛机

DOI：
10.1038/s42005-022-01111-x
发表时间：
2022
期刊：
Communications Physics
影响因子：
5.5
作者：
English, L. Q.;Zampetaki, A. V.;Kalinin, K. P.;Berloff, N. G.;Kevrekidis, P. G.
通讯作者：
Kevrekidis, P. G.

Solitary waves in a quantum droplet-bearing system

DOI：
10.1103/physreva.107.063308
发表时间：
2023-02
期刊：
Physical Review A
影响因子：
2.9
作者：
G. Katsimiga;S. Mistakidis;G. N. Koutsokostas;D. Frantzeskakis;R. Carretero-González;P. Kevrekidis
通讯作者：
G. Katsimiga;S. Mistakidis;G. N. Koutsokostas;D. Frantzeskakis;R. Carretero-González;P. Kevrekidis

A spectral analysis of the nonlinear Schrödinger equation in the co-exploding frame

共爆框架下非线性薛定谔方程的谱分析

DOI：
10.1016/j.physd.2022.133396
发表时间：
2022
期刊：
Physica D: Nonlinear Phenomena
影响因子：
0
作者：
Chapman, S.J.;Kavousanakis, M.;Charalampidis, E.G.;Kevrekidis, I.G.;Kevrekidis, P.G.
通讯作者：
Kevrekidis, P.G.