Inverse Scattering Theory
Inverse Scattering Theory
批准号:
0071398
负责人:
Xin Zhou
金额:
$8.8万
依托单位:
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
项目状态:
已结题
起止时间:
2000-07-01 至 2003-06-30
中文摘要
DMS-0071398项目包含五个研究问题:1.散射/逆散射变换的分析性质. NLS上的扰动。3.户田晶格的微扰.随机矩阵。多个正交多项式。 所有这些问题都将通过Riemann-Hilbert问题方法进行研究,该方法在解决各种广义可积问题方面显示出巨大的潜力。该项目分析了从偏微分方程、随机矩阵到逼近理论等多个数学问题。这些问题有的是纯理论性的,有的是在物理和工程上有应用的,其中之一就是微扰非线性薛定谔方程的孤子解。这些孤子解可用于光纤传输。
英文摘要
DMS-0071398The project contains five research problems:1. Analytic properties for scattering/inverse scatteringtransforms.2. Perturbation on NLS.3. Perturbation for Toda lattice.4. Random matrices.5. Multiple orthogonal polynomials. All these problems will be studied via the Riemann--Hilbertproblem approach, which has shown tremendous potential insolving various integrable problems in broad sense.This project analyzes several mathematical problems rangingfrom partial differential equations, random matrices, to the approximation theory. Some of these problems have pure mathematicalinterest and others have applications in physics and engineering.One of such applications is the soliton solutions of the perturbednonlinear Schrodinger equation. These soliton solutions are usedin the fiber optical transmission.
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会议论文
CAREER:New Development in Geometric Variational Theory
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批准号:2243149
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项目类别:Continuing Grant
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资助金额:$46.15万
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财政年份:2022
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负责人:Xin Zhou
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依托单位:
CAREER:New Development in Geometric Variational Theory
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批准号:1945178
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项目类别:Continuing Grant
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资助金额:$46.15万
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财政年份:2020
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负责人:Xin Zhou
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依托单位:
Geometric Variational Theory and Application
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批准号:1811293
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项目类别:Standard Grant
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资助金额:$16.2万
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财政年份:2018
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负责人:Xin Zhou
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依托单位:
Investigation on Differential Geometry and General Relativity
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批准号:1704393
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项目类别:Standard Grant
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资助金额:$5.2万
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财政年份:2016
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负责人:Xin Zhou
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依托单位:
Investigation on Differential Geometry and General Relativity
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批准号:1406337
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项目类别:Standard Grant
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资助金额:$13.73万
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财政年份:2014
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负责人:Xin Zhou
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依托单位:
Riemann-Hilbert Problem and Integrable Systems
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批准号:0602344
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项目类别:Standard Grant
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资助金额:$12.54万
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财政年份:2006
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负责人:Xin Zhou
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依托单位:
Riemann-Hilbert problem and integrable systems
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批准号:0300844
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项目类别:Standard Grant
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资助金额:$12.6万
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财政年份:2003
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负责人:Xin Zhou
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依托单位:
Inverse Scattering Theory
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批准号:9706644
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项目类别:Standard Grant
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资助金额:$8.04万
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财政年份:1997
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负责人:Xin Zhou
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依托单位:
Mathematical Sciences: Inverse Scattering Theory
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批准号:9401403
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项目类别:Standard Grant
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资助金额:$5.5万
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财政年份:1994
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负责人:Xin Zhou
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依托单位:
Mathematical Sciences: Inverse Scattering Theory
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批准号:9204804
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项目类别:Standard Grant
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资助金额:$4.4万
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财政年份:1992
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负责人:Xin Zhou
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依托单位:
Mathematical Sciences: Inverse Scattering Theory
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批准号:9000054
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项目类别:Standard Grant
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资助金额:$1.22万
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财政年份:1990
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负责人:Xin Zhou
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依托单位:
Mathematical Sciences: Inverse Scattering Theory
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批准号:9196033
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项目类别:Standard Grant
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资助金额:$1.92万
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财政年份:1990
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负责人:Xin Zhou
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依托单位:
国内基金
海外基金
Lagrangian origin of geometric approaches to scattering amplitudes
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批准号:24ZR1450600
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项目类别:省市级项目
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资助金额:--
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批准年份:2024
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负责人:ALEXANDER OCHIROV
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依托单位:
微波有源Scattering dark state粒子的理论及应用研究
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批准号:61701437
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项目类别:青年科学基金项目
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资助金额:28.0万元
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批准年份:2017
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负责人:李欢
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依托单位: