Most cited papers in Advanced Mathematical Physics Problems
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).
Showing 50 of 97 papers. Every paper with more than 590 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Hitchhikerʼs guide to the fractional Sobolev spaces Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci · Bulletin des Sciences Mathématiques | 29 Dec 2011 | 4,369 |
| 2 | An integrable shallow water equation with peaked solitons Roberto Camassa, Darryl D. Holm · Physical Review Letters | 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 | 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 | 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 |
| 6 | Endpoint Strichartz estimates M. Keel, Terence Tao · American Journal of Mathematics | Oct 1998 | 2,081 |
| 7 | Ordinary differential equations, transport theory and Sobolev spaces Ronald J. DiPerna, Pierre Louis Lions · Inventiones mathematicae | Oct 1989 | 2,007 |
| 8 | Weak solutions of nonlinear hyperbolic equations and their numerical computation Peter D. Lax · Communications on Pure and Applied Mathematics | Feb 1954 | 1,851 |
| 9 | Existence of solitary waves in higher dimensions Walter A. Strauss · Communications in Mathematical Physics | Jun 1977 | 1,834 |
| 10 | Operator expansion for high-energy scattering Ian Balitsky · Nuclear Physics B | Mar 1996 | 1,809 |
| 11 | Quantum sine-Gordon equation as the massive Thirring model Sidney Coleman · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields | 15 Apr 1975 | 1,776 |
| 12 | Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations Jean Bourgain · Geometric and Functional Analysis | May 1993 | 1,697 |
| 13 | Nonlinear Dispersive Equations Terence Tao · Regional conference series in mathematics | 8 Jun 2006 | 1,603 |
| 14 | Remarks on the breakdown of smooth solutions for the 3-D Euler equations J. Thomas Beale, T. Kato, Andrew J. Majda · Communications in Mathematical Physics | Mar 1984 | 1,592 |
| 15 | On a class of nonlinear Schr�dinger equations Paul H. Rabinowitz · Zeitschrift für angewandte Mathematik und Physik | Mar 1992 | 1,585 |
| 16 | The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2 Pierre‐Louis Lions · Annales de l Institut Henri Poincaré C Analyse Non Linéaire | Aug 1984 | 1,583 |
| 17 | Wave breaking for nonlinear nonlocal shallow water equations Adrian Constantin, Joachim Escher · Acta Mathematica | 1998 | 1,499 |
| 18 | Universality and scaling in gravitational collapse of a massless scalar field Matthew W. Choptuik · Physical Review Letters | 4 Jan 1993 | 1,458 |
| 19 | Nonlinear Schr�dinger equations and sharp interpolation estimates Michael I. Weinstein · Communications in Mathematical Physics | Dec 1983 | 1,451 |
| 20 | Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations Shikuo Liu, Shikuo Liu, Zuntao Fu et al. · Physics Letters A | Oct 2001 | 1,436 |
| 21 | Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle Carlos E. Kenig, Gustavo Henrique Santos Flores Ponce, Luis Vega · Communications on Pure and Applied Mathematics | Apr 1993 | 1,417 |
| 22 | Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems Flore K. Kunst, Elisabet Edvardsson, Jan Carl Budich et al. · Physical Review Letters | 11 Jul 2018 | 1,416 |
| 23 | StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions Tosio Kato · Mathematische Zeitschrift | Dec 1984 | 1,348 |
| 24 | Global and local behavior of positive solutions of nonlinear elliptic equations Basilis Gidas, Joel Spruck · Communications on Pure and Applied Mathematics | Jul 1981 | 1,319 |
| 25 | Stability theory of solitary waves in the presence of symmetry, II Manoussos G. Grillakis, Jalal Shatah, Walter A. Strauss · Journal of Functional Analysis | Dec 1990 | 1,296 |
| 26 | Time dependent boundary conditions for hyperbolic systems Kevin W. Thompson · Journal of Computational Physics | 1987 | 1,188 |
| 27 | C1 + α local regularity of weak solutions of degenerate elliptic equations Emmanuele DiBenedetto · Nonlinear Analysis | 1983 | 1,137 |
| 28 | Stability theory of solitary waves in the presence of symmetry, I Manoussos G. Grillakis, Jalal Shatah, Walter A. Strauss · Journal of Functional Analysis | Sep 1987 | 1,109 |
| 29 | Orbital stability of standing waves for some nonlinear Schr�dinger equations Thierry Cazenave, Pierre‐Louis Lions · Communications in Mathematical Physics | Dec 1982 | 1,098 |
| 30 | Nonlinear-Evolution Equations of Physical Significance Mark J. Ablowitz, David J. Kaup, Alan C. Newell et al. · Physical Review Letters | 9 Jul 1973 | 1,095 |
| 31 | A discrete transform and decompositions of distribution spaces Michael Frazier, Bjorn D. Jawerth · Journal of Functional Analysis | Oct 1990 | 1,046 |
| 32 | On the interior regularity of weak solutions of the Navier-Stokes equations James B Serrin · Archive for Rational Mechanics and Analysis | 1962 | 1,044 |
| 33 | The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations Adrian Constantin, David Lannes · Archive for Rational Mechanics and Analysis | 29 May 2008 | 1,030 |
| 34 | Subelliptic estimates and function spaces on nilpotent Lie groups Gerald B. Folland · Arkiv för matematik | Dec 1975 | 1,022 |
| 35 | A connection between nonlinear evolution equations and ordinary differential equations of P-type. I Mark J. Ablowitz, A. Ramani, Harvey Segur · Journal of Mathematical Physics | Apr 1980 | 1,016 |
| 36 | Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics Mingliang Wang, Yubin Zhou, Zhibin Li · Physics Letters A | Jun 1996 | 991 |
| 37 | Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group Gerald B. Folland, E. M. Stein · Communications on Pure and Applied Mathematics | Jul 1974 | 982 |
| 38 | Solitary wave solutions for variant Boussinesq equations Mingliang Wang · Physics Letters A | Mar 1995 | 974 |
| 39 | Renormalization group flows from holography: Supersymmetry and a $c$-theorem Daniel Z. Freedman, Steven S. Gubser, Krzysztof Pilch et al. · Advances in Theoretical and Mathematical Physics | 1999 | 962 |
| 40 | Stability of peakons Adrian Constantin, Walter A. Strauss · Communications on Pure and Applied Mathematics | May 2000 | 957 |
| 41 | Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities Élliott H. Lieb | 2002 | 946 |
| 42 | Nonlinear differential−difference equations Mark J. Ablowitz, J. F. Ladik · Journal of Mathematical Physics | Mar 1975 | 941 |
| 43 | Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids Sergiù Klainerman, Andrew J. Majda · Communications on Pure and Applied Mathematics | Jul 1981 | 940 |
| 44 | Method for Solving the Sine-Gordon Equation Mark J. Ablowitz, David J. Kaup, Alan C. Newell et al. · Physical Review Letters | 18 Jun 1973 | 940 |
| 45 | Inverse scattering on the line Percy A. Deift, Eugene Trubowitz · Communications on Pure and Applied Mathematics | Mar 1979 | 929 |
| 46 | Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity Igor R. Klebanov, Edward H. Witten | 1998 | 919 |
| 47 | Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system Yoshikazu Giga · Journal of Differential Equations | Apr 1986 | 910 |
| 48 | Lyapunov stability of ground states of nonlinear dispersive evolution equations Michael I. Weinstein · Communications on Pure and Applied Mathematics | 1986 | 903 |
| 49 | Well-posedness for the Navier–Stokes Equations Herbert Koch, Daniel Tataru · Advances in Mathematics | 2001 | 892 |
| 50 | Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics Vitaly Moroz, Jean Van Schaftingen · Journal of Functional Analysis | 28 Apr 2013 | 886 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.