Leaderboards/Advanced Mathematical Physics Problems

Advanced Mathematical Physics Problems

Last updated July 7, 2026

Rising Stars

New and hot

Rising Stars Researchers

1
Timothée Crin-Barat
Laboratoire d’Analyse et de Mathématiques Appliquées
2
Marcelo V. Flamarion
Pontificia Universidad Católica del Perú
3
Yiling Yang
Fudan University
4
Brij Mohan
University of Delhi
5
Thomas Alazard
Centre de Mathématiques Laurent Schwartz
6
T. Congy
Northumbria University
7
Ruizhi Gong
Beijing Information Science & Technology University
8
Wen Feng
Xi'an Jiaotong University
9
Andrea Dei
Fermi National Accelerator Laboratory
10
Lihua Dong
Nanjing Tech University

Rising Stars Papers

1
Generalization and analytic exploration of soliton solutions for nonlinear evolution equations via a novel symbolic approach in fluids and nonlinear sciences
Chinese Journal of Physics|2024
75 cit.
2
Painlevé analysis, restricted bright-dark N-solitons, and N-rogue waves of a (4+1)-dimensional variable-coefficient generalized KP equation in nonlinear sciences
Nonlinear Dynamics|2024
58 cit.
3
On investigation of kink-solitons and rogue waves to a new integrable (3+1)-dimensional KdV-type generalized equation in nonlinear sciences
Nonlinear Dynamics|2024
47 cit.
4
Bilinearization and new center-controlled N-rogue solutions to a (3+1)-dimensional generalized KdV-type equation in plasmas via direct symbolic approach
Nonlinear Dynamics|2024
44 cit.
5
Rogue-wave structures for a generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles
Physica Scripta|2024
27 cit.
6
Statistics of Extreme Events in Integrable Turbulence
Physical Review Letters|2024
22 cit.
7
Solving AdS3 string theory at minimal tension: tree-level correlators
Journal of High Energy Physics|2024
20 cit.
8
Non-integrable soliton gas: The Schamel equation framework
Chaos Solitons & Fractals|2024
19 cit.
9
Tensionless AdS3/CFT2 and single trace $$ T\overline{T} $$
Journal of High Energy Physics|2024
17 cit.
10
Topological Constraints on the Dynamics of Vortex Formation in a Two-Dimensional Quantum Fluid
Physical Review Letters|2024
11 cit.

Emerging Leaders

Gaining momentum

Emerging Leaders Researchers

1
Yi Zhu
East China University of Science and Technology
2
In‐Jee Jeong
Korea Institute for Advanced Study
3
Weiren Zhao
Zhejiang University
4
Yakov Shlapentokh-Rothman
University of Toronto
5
Khaled Zennir
Qassim University
6
Motohiro Sobajima
Tokyo University of Science
7
Weipeng Zhu
Foshan University
8
Xuexiu Zhong
South China Normal University
9
Yanghai Yu
Anhui Normal University
10
Xiao-Tian Gao
Beijing University of Posts and Telecommunications

Emerging Leaders Papers

1
N-soliton, Hth-order breather, hybrid and multi-pole solutions for a generalized variable-coefficient Gardner equation with an external force in a plasma or fluid
Nonlinear Dynamics|2024
154 cit.
2
Bilinear Bäcklund Transformations, as well as N-Soliton, Breather, Fission/Fusion and Hybrid Solutions for a (3+1)-Dimensional Integrable Wave Equation in a Fluid
Qualitative Theory of Dynamical Systems|2025
124 cit.
3
Auto-Bäcklund transformations and soliton solutions on the nonzero background for a (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation in a fluid
Nonlinear Dynamics|2023
111 cit.
4
N-fold Darboux transformation and solitonic interactions for the Kraenkel–Manna–Merle system in a saturated ferromagnetic material
Nonlinear Dynamics|2022
103 cit.
5
Similarity Reductions on a (2$$+$$1)-Dimensional Variable-Coefficient Modified Kadomtsev-Petviashvili System Describing Certain Electromagnetic Waves in a Thin Film
International Journal of Theoretical Physics|2024
96 cit.
6
Normalized solution to the Schrödinger equation with potential and general nonlinear term: Mass super-critical case
Journal of Differential Equations|2022
73 cit.
7
Stability threshold of two-dimensional Couette flow in Sobolev spaces
Annales de l Institut Henri Poincaré C Analyse Non Linéaire|2022
67 cit.
8
Shallow-water-wave studies on a (2 + 1)-dimensional Hirota–Satsuma–Ito system: X-type soliton, resonant Y-type soliton and hybrid solutions
Chaos Solitons & Fractals|2022
65 cit.
9
Considering the Shallow Water of a Wide Channel or an Open Sea Through a Generalized (2+1)-dimensional Dispersive Long-wave System
Qualitative Theory of Dynamical Systems|2022
58 cit.
10
Lump and hybrid solutions for a (3+1)-dimensional Boussinesq-type equation for the gravity waves over a water surface
Chinese Journal of Physics|2023
52 cit.

Current Senior Leaders

Established & currently active

Current Senior Leaders Researchers

1
Luis Vega
Universidad de Guanajuato
2
Walter A. Strauss
Brown University
3
Terence Tao
University of California, Los Angeles
4
Zhi-Qiang Wang
Utah State University
5
Enrico Valdinoci
The University of Western Australia
6
Daniel Tataru
Northwestern University
7
Jiahong Wu
University of Notre Dame
8
Andrew J. Majda
New York University Abu Dhabi
9
Edriss S. Titi
University of Cambridge
10
Zhouping Xin
Chinese University of Hong Kong

Current Senior Leaders Papers

1
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
IEEE Transactions on Information Theory|2006
15.8k cit.
2
Decoding by Linear Programming
IEEE Transactions on Information Theory|2005
7.3k cit.
3
Stable signal recovery from incomplete and inaccurate measurements
Communications on Pure and Applied Mathematics|2006
7.2k cit.
4
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory|2006
6.9k cit.
5
Hitchhikerʼs guide to the fractional Sobolev spaces
Bulletin des Sciences Mathématiques|2011
4.3k cit.
6
Absorbing boundary conditions for the numerical simulation of waves
Mathematics of Computation|1977
2.4k cit.
7
The Power of Convex Relaxation: Near-Optimal Matrix Completion
IEEE Transactions on Information Theory|2010
2.1k cit.
8
Endpoint Strichartz estimates
American Journal of Mathematics|1998
2.1k cit.
9
Existence of solitary waves in higher dimensions
Communications in Mathematical Physics|1977
1.8k cit.
10
Remarks on the breakdown of smooth solutions for the 3-D Euler equations
Communications in Mathematical Physics|1984
1.6k cit.

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