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Topic · Mathematical Physics

Advanced Mathematical Physics Problems

Advanced Mathematical Physics Problems is a research topic within Mathematical Physics. Science Explorer counts 22k research works in it since 1951. 20.7% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the global well-posedness, scattering, and blow-up phenomena for various nonlinear wave equations, including the nonlinear Schrödinger equation, wave maps equation, Korteweg-de Vries equation, and dispersive equations. The research also explores the behavior of solitons and critical exponent for energy-critical equations.

  • Global Well-Posedness
  • Nonlinear Schrödinger Equation
  • Scattering
  • Blow-Up
  • Dispersive Equations
  • Strichartz Estimates
  • Energy-Critical Equations
  • Wave Maps Equation
  • Korteweg-de Vries Equation
  • Solitons
Research works
22k
fractional, since 1951
In the world top 10%
4.6k
per year above
Top-10% rate
20.7%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+23%
the tick is no change

Which countries lead Advanced Mathematical Physics Problems research?

By volume, China and the United States publish the most (1.8k and 340 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 1.8k works
  2. 2 United States 340 works
  3. 3 France 240 works
  4. 4 Japan 182 works
  5. 5 Italy 161 works
  6. 6 Russia 140 works
  7. 7 Brazil 132 works
  8. 8 Saudi Arabia 105 works
  9. 9 Germany 101 works
  10. 10 India 99 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 55.1%United States: 10.2%France: 7.2%Japan: 5.5%6 others listed: 22.1%55%largest
China1,844 · 55.1%United States340 · 10.2%France240 · 7.2%Japan182 · 5.5%6 others listed738 · 22.1%

Shares of the rows listed above, not of the whole node.

Which institutions lead Advanced Mathematical Physics Problems research?

By volume in 2022–2025, Southwest University publishes the most Advanced Mathematical Physics Problems research, followed by Centre National de la Recherche Scientifique and Zhejiang Normal University.

By volume, 2022–2025

  1. 1 Southwest UniversityChina 42 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 39 works
  3. 3 Zhejiang Normal UniversityChina 38 works
  4. 4 Central South UniversityChina 37 works
  5. 5 Beijing Normal UniversityChina 30 works
  6. 6 Fudan UniversityChina 27 works
  7. 7 China University of Mining and TechnologyChina 24 works
  8. 8 Central China Normal UniversityChina 23 works
  9. 9 Tsinghua UniversityChina 21 works
  10. 10 Qassim UniversitySaudi Arabia 20 works

Who are the leading researchers in Advanced Mathematical Physics Problems?

The most-cited researchers publishing on Advanced Mathematical Physics Problems include Tasawar Hayat, Terence Tao and Miroslav Krstić.

  1. 1 Tasawar Hayat Pakistan 4.6k citations
  2. 2 Terence Tao United States 3.1k citations
  3. 3 Miroslav Krstić United States 3.1k citations
  4. 4 Élliott H. Lieb United States 2.5k citations
  5. 5 George H. Weiss United States 2.4k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is Advanced Mathematical Physics Problems research done?

The largest centres of Advanced Mathematical Physics Problems research in 2022–2025 are Beijing (China), Shanghai (China), Guangzhou (China) and Nanjing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Jinhua and Buraidah.

Largest cities, 2022–2025

  1. 1 Beijing China 281 works
  2. 2 Shanghai China 123 works
  3. 3 Guangzhou China 91 works
  4. 4 Nanjing China 85 works
  5. 5 Paris France 80 works
  6. 6 Chongqing China 70 works
  7. 7 Wuhan China 68 works
  8. 8 Moscow Russia 63 works
  9. 9 Changsha China 58 works
  10. 10 Tokyo Japan 56 works

Where it is the local speciality

  1. JinhuaCN · 38.5 works24×
  2. BuraidahSA · 21.3 works17×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Advanced Mathematical Physics Problems than the world average.

See Advanced Mathematical Physics Problems on the map

Where is the best place to study Advanced Mathematical Physics Problems?

Among universities, judged by research, Beijing Normal University, Taibah University and Qassim University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 24.47%fractional works in this node (log) →share in the world top 10% →Beijing Normal University: 30, 36.6%Taibah University: 10, 28.5%Qassim University: 20, 14.0%Southwest University: 42, 18.3%Université Sultan Moulay Slimane: 10, 38.3%Zhejiang Normal University: 38, 17.2%Guangzhou University: 18, 19.3%Central South University: 37, 18.4%Changchun Normal University: 8, 36.4%Qufu Normal University: 12, 17.7%Beijing Normal Unive…Taibah UniversitySouthwest UniversityQassim University
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Beijing Normal UniversityChina 76.336.6%10.1×30 +10.6%
2 Taibah UniversitySaudi Arabia 74.428.5%15.1×10 +222.9%
3 Qassim UniversitySaudi Arabia 70.814.0%18.3×20 +584.4%
4 Southwest UniversityChina 69.318.3%18.0×42 +91.5%
5 Université Sultan Moulay SlimaneMorocco 66.438.3%17.7×10 —
6 Zhejiang Normal UniversityChina 63.217.2%31.0×38 -1.9%
7 Guangzhou UniversityChina 61.319.3%11.6×18 +86.2%
8 Central South UniversityChina 61.218.4%5.2×37 +336.5%
9 Changchun Normal UniversityChina 60.136.4%60.2×8 —
10 Qufu Normal UniversityChina 58.617.7%15.2×12 +283.3%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Advanced Mathematical Physics Problems research growing?

Output in 2018–2022 was 23% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Advanced Mathematical Physics Problems.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.