RUI: Mathematical Analysis of Several Models in Nonlinear Optics

RUI:非线性光学中几种模型的数学分析

基本信息

  • 批准号:
    1715991
  • 负责人:
  • 金额:
    $ 12.12万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2017
  • 资助国家:
    美国
  • 起止时间:
    2017-08-15 至 2022-07-31
  • 项目状态:
    已结题

项目摘要

The most recent advances in nonlinear optics include the generation and applications of ultrashort optical pulses, whose time duration is typically of the order of femtoseconds (one quadrillionth of a second). Duration of these pulses is approaching the timescales of fundamental atomic and molecular processes. They deliver energy so quickly that it allows them to probe living structures without damage and to make material modifications on the micron scale with minimal heat effects. Femtoscale lasers are used, for example, in microsurgery or materials processing. For ultrashort pulses, the traditional mathematical models used for longer optical pulses, the Nonlinear Schrödinger (NLS) and Coupled Nonlinear Schrödinger (CNLS) equations, lose their predictive capabilities. This research project is concerned with two novel mathematical models: the Complex Short Pulse (CSP) equation and the Coupled Complex Short Pulse (CCSP) equation. The project is devoted to analysis and computation of solutions of these equations for the description of ultrashort optical pulses.The models to be investigated are integrable; the project concerns the investigation of the CSP equation, the CCSP equation and their integrable semi-discrete analogues, where the spatial variable takes values in a lattice, while the integrability of the resulting equations is preserved. In particular, the investigator plans to: (1) construct the semi-discrete CSP equation and derive exact solutions including bright and dark solitons and rogue-wave-like solutions; (2) construct bright-bright, dark-dark and bright-dark (mixed) soliton solutions, as well as rogue wave solutions, of the CCSP equation; (3) utilize the semi-discrete CSP equation as a novel self-adaptive moving mesh numerical method for simulating solutions of the continuous CSP model. Being at the second largest Hispanic-serving institution in the country, the investigator strives to motivate and encourage undergraduate and graduate students to engage in cutting-edge research in applied mathematics.
非线性光学的最新进展包括超短光脉冲的产生和应用,其持续时间通常为飞秒(千万亿分之一秒)的量级。这些脉冲的持续时间接近基本原子和分子过程的时间尺度。它们传递能量的速度如此之快,以至于它们可以在不损坏生命结构的情况下探测生命结构,并以最小的热效应在微米尺度上进行材料修改。例如,飞秒激光用于显微外科手术或材料处理。对于超短脉冲,用于较长光脉冲的传统数学模型,非线性薛定谔(NLS)和耦合非线性薛定谔(CNLS)方程,失去了预测能力。本研究计划主要探讨两种新的数学模型:复短脉冲(CSP)方程和耦合复短脉冲(CCSP)方程。该项目致力于分析和计算用于描述超短光脉冲的这些方程的解。要研究的模型是可积的;该项目涉及CSP方程、CCSP方程及其可积半离散类似物的研究,其中空间变量在格中取值,而所得方程的可积性保持不变。 具体地说,研究者计划:(1)构造半离散的CSP方程,并导出包括亮孤子、暗孤子和类Rogue波解在内的精确解:(2)构造CCSP方程的亮-亮、暗-暗和亮-暗(混合)孤子解以及类Rogue波解;(3)利用半离散CSP方程作为一种新的自适应移动网格数值方法,模拟连续CSP模型的解。作为在该国第二大西班牙裔服务机构,调查员努力激励和鼓励本科生和研究生从事应用数学的前沿研究。

项目成果

期刊论文数量(17)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Darboux transformation and solitonic solution to the coupled complex short pulse equation
  • DOI:
    10.1016/j.physd.2022.133332
  • 发表时间:
    2021-10
  • 期刊:
  • 影响因子:
    0
  • 作者:
    B. Feng;Liming Ling
  • 通讯作者:
    B. Feng;Liming Ling
Multi-breather solutions to the Sasa–Satsuma equation
  • DOI:
    10.1098/rspa.2021.0711
  • 发表时间:
    2021-11
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Chengfa Wu;Bo Wei;Changyan Shi;Bao-Feng Feng-Bao-Feng-Feng-2264833290
  • 通讯作者:
    Chengfa Wu;Bo Wei;Changyan Shi;Bao-Feng Feng-Bao-Feng-Feng-2264833290
General soliton solutions to the nonlocal nonlinear Schrödinger equation
非局部非线性薛定谔方程的一般孤子解
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    1.7
  • 作者:
    Feng, Bao-Feng;Ablowitz, Mark;Luo Xu-Dan, Musslimani Ziad
  • 通讯作者:
    Luo Xu-Dan, Musslimani Ziad
Tau‐function formulation for bright, dark soliton and breather solutions to the massive Thirring model
  • DOI:
    10.1111/sapm.12532
  • 发表时间:
    2022-08
  • 期刊:
  • 影响因子:
    2.7
  • 作者:
    Junchao Chen;B. Feng
  • 通讯作者:
    Junchao Chen;B. Feng
General breather and rogue wave solutions to the complex short pulse equation
  • DOI:
    10.1016/j.physd.2022.133360
  • 发表时间:
    2022-06
  • 期刊:
  • 影响因子:
    0
  • 作者:
    B. Feng;Ruyun Ma;Yujuan Zhang
  • 通讯作者:
    B. Feng;Ruyun Ma;Yujuan Zhang
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Baofeng Feng其他文献

A stabilized self-adaptive moving mesh integrator for the short pulse equation
短脉冲方程稳定自适应动网格积分器
  • DOI:
  • 发表时间:
    2016
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Shun Sato;Takayasu Matsuo;Baofeng Feng
  • 通讯作者:
    Baofeng Feng
Rogue waves in the massive Thirring modelStud Appl Math
  • DOI:
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
  • 作者:
    Junchao Chen;Bo Yang;Baofeng Feng
  • 通讯作者:
    Baofeng Feng
Convergence analysis of a conservative finite difference scheme for the modified Hunter--Saxton equation
修正Hunter--Saxton方程保守有限差分格式的收敛性分析
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Shun Sato;Kazuhito Oguma;Takayasu Matsuo;Baofeng Feng;佐藤 峻;佐藤 峻;Shun Sato
  • 通讯作者:
    Shun Sato
modified Hunter--Saxton方程式に対する保存的数値解法と爆発現象の数値的観察
修正亨特--萨克斯顿方程的保守数值解及爆炸现象的数值观测
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Shun Sato;Kazuhito Oguma;Takayasu Matsuo;Baofeng Feng;佐藤 峻;佐藤 峻;Shun Sato;佐藤 峻
  • 通讯作者:
    佐藤 峻
Numerical and theoretical treatment of evolutionary differential equations with a mixed derivative
具有混合导数的演化微分方程的数值和理论处理
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Shun Sato;Kazuhito Oguma;Takayasu Matsuo;Baofeng Feng;佐藤 峻;佐藤 峻;Shun Sato;佐藤 峻;Shun Sato
  • 通讯作者:
    Shun Sato

Baofeng Feng的其他文献

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{{ truncateString('Baofeng Feng', 18)}}的其他基金

CBMS Conference: Discrete Painleve Equations
CBMS 会议:离散 Painleve 方程
  • 批准号:
    1543860
  • 财政年份:
    2016
  • 资助金额:
    $ 12.12万
  • 项目类别:
    Standard Grant

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  • 批准号:
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  • 财政年份:
    1987
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