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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. 10.0% 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%
2.2k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+23%
the tick is no change
Largest producer
China
56% of the 10 largest, 2022-now
Advanced Mathematical Physics Problems

Which countries lead Advanced Mathematical Physics Problems research?

By volume, China and the United States publish the most (2k and 364 works in 2022-now).

By volume, 2022-now

  1. 1 China 2k works
  2. 2 United States 364 works
  3. 3 France 251 works
  4. 4 Japan 194 works
  5. 5 Italy 169 works
  6. 6 Brazil 145 works
  7. 7 Russia 145 works
  8. 8 Saudi Arabia 116 works
  9. 9 Germany 106 works
  10. 10 India 103 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: 55.5%United States: 10.2%France: 7.0%Japan: 5.4%6 others listed: 21.9%56%largest
China1,989 · 55.5%United States364 · 10.2%France251 · 7.0%Japan194 · 5.4%6 others listed784 · 21.9%

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

Which institutions lead Advanced Mathematical Physics Problems research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Mathematical Physics Problems research, followed by Russian Academy of Sciences and Chinese Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 128 works
  2. 2 Russian Academy of SciencesRussia 52 works
  3. 3 Chinese Academy of SciencesChina 44 works
  4. 4 Southwest UniversityChina 44 works
  5. 5 Zhejiang Normal UniversityChina 40 works
  6. 6 Central South UniversityChina 38 works
  7. 7 Beijing Normal UniversityChina 32 works
  8. 8 Fudan UniversityChina 29 works
  9. 9 China University of Mining and TechnologyChina 25 works
  10. 10 Tsinghua UniversityChina 25 works

Who are the leading researchers in Advanced Mathematical Physics Problems?

The most-cited researchers publishing on Advanced Mathematical Physics Problems include Edward H. Witten, Tasawar Hayat and M. Williams.

  1. 1 Edward H. Witten United States 174k citations
  2. 2 Tasawar Hayat Pakistan 135k citations
  3. 3 M. Williams France 134k citations

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

What are the most cited papers in Advanced Mathematical Physics Problems?

The most cited paper in Advanced Mathematical Physics Problems is "Hitchhikerʼs guide to the fractional Sobolev spaces" (Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci, 2011), with 4,369 citations. Next come "An integrable shallow water equation with peaked solitons" (3,754) and "Nonlinear scalar field equations, I existence of a ground state" (2,626).

Most cited papers
#PaperReleasedCitations
1 Hitchhikerʼs guide to the fractional Sobolev spaces Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci · Bulletin des Sciences Mathématiques Open access 29 Dec 2011 4,369
2 An integrable shallow water equation with peaked solitons Roberto Camassa, Darryl D. Holm · Physical Review Letters Open access 13 Sep 1993 3,754
3 Nonlinear scalar field equations, I existence of a ground state Henri Berestycki, P. L. Lions · Archive for Rational Mechanics and Analysis Open access Dec 1983 2,626
4 The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. Pierre‐Louis Lions · Annales de l Institut Henri Poincaré C Analyse Non Linéaire Open access Apr 1984 2,409
5 Model equations for long waves in nonlinear dispersive systems Thomas Brooke Benjamin, Jerry L. Bona, J. J. Mahony · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences 30 Mar 1972 2,098
All 97 most cited papers, with filters and sorting

Where is Advanced Mathematical Physics Problems research done?

The largest centres of Advanced Mathematical Physics Problems research in 2022-now 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-now

  1. 1 BeijingChina 298 works
  2. 2 ShanghaiChina 132 works
  3. 3 GuangzhouChina 96 works
  4. 4 NanjingChina 91 works
  5. 5 ParisFrance 84 works
  6. 6 WuhanChina 72 works
  7. 7 ChongqingChina 72 works
  8. 8 MoscowRussia 66 works
  9. 9 ChangshaChina 61 works
  10. 10 TokyoJapan 59 works

Where it is the local speciality

  1. JinhuaCN · 40.5 works24×
  2. BuraidahSA · 25.6 works19×
← 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, Taibah University, Beijing Normal University and Zhejiang Normal 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 18.67%fractional works in this field (log) →share of work in the world top 10% →Taibah UniversityBeijing Normal Unive…Qassim UniversityZhejiang Normal Univ…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Taibah UniversitySaudi Arabia 73.133.9%16.8×10 +14.4%
2Beijing Normal UniversityChina 66.521.3%9.9×32 +40.5%
3Zhejiang Normal UniversityChina 65.814.7%35.2×40 +123.3%
4Qassim UniversitySaudi Arabia 60.815.4%23.3×24 +11.0%
5China University of Mining and TechnologyChina 58.018.2%8.1×26 +98.5%
6Beijing University of Posts and TelecommunicationsChina 57.336.3%4.2×11 +51.5%
7Central South UniversityChina 57.29.7%4.9×38 +20.1%
8Southwest UniversityChina 57.05.8%20.1×44 +47.2%
9Tsinghua UniversityChina 54.918.3%2.6×25 +48.8%
10Fudan UniversityChina 53.613.1%4.6×29 +47.7%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Advanced Mathematical Physics Problems, country by country

Is Advanced Mathematical Physics Problems research growing?

Output in 2022-2025 was 23% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Advanced Mathematical Physics Problems.

still counting19801990200020102020
grewheldshrank

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

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Advanced Mathematical Physics Problems as a percentage of every work published that year, 0.022% in 2024.

still counting0.010%0.020%0.030%Advanced Mathematical Physics Problems0.018% in 202519801990200020102020

Fractional works of Advanced Mathematical Physics Problems over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Advanced Mathematical Physics Problems9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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