Martin David Kruskal | Academic Influence

Martin David Kruskal's AcademicInfluence.com Rankings

Martin David Kruskal

Mathematics

#1305

World Rank

#2183

Historical Rank

#544

USA Rank

Measure Theory

#746

World Rank

#1003

Historical Rank

#296

USA Rank

mathematics Degrees

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Mathematics

Martin David Kruskal's Degrees

PhD Mathematics New York University

Why Is Martin David Kruskal Influential?

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According to Wikipedia, Martin David Kruskal was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis. His most celebrated contribution was in the theory of solitons.

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Martin David Kruskal's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Method for solving the Korteweg-deVries equation (1967) (3668)
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States (1965) (3254)
An energy principle for hydromagnetic stability problems (1958) (1082)
Exact Nonlinear Plasma Oscillations (1957) (1039)
New similarity reductions of the Boussinesq equation (1989) (901)
Korteweg‐de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion (1968) (813)
Korteweg-devries equation and generalizations. VI. methods for exact solution (1974) (739)
Maximal extension of Schwarzschild metric (1960) (637)
Equilibrium of a Magnetically Confined Plasma in a Toroid (1958) (416)
Some instabilities of a completely ionized plasma (1954) (379)
Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly Periodic (1962) (361)
On the Stability of Plasma in Static Equilibrium (1958) (289)
Kink dynamics in the highly discrete sine-Gordon system (1984) (271)
Painlevé test for the self-dual Yang-Mills equation (1982) (201)
Korteweg‐deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws (1970) (178)
Asymptotics beyond all orders in a model of crystal growth (1991) (163)
Asymptotics beyond all orders (1987) (137)
Hydromagnetic instability in a stellarator (1958) (119)
Solitary wave collisions (1979) (115)
The Painlevé‐Kowalevski and Poly‐Painlevé Tests for Integrability (1992) (112)
A two-parameter Miura transformation of the Benjamin-Ono equation (1979) (106)
Stroboscopic‐Perturbation Procedure for Treating a Class of Nonlinear Wave Equations (1964) (96)
The instability of a pinched fluid with a longitudinal magnetic field (1958) (90)
Nonlinear wave equations (1975) (87)
Topics in soliton theory and exactly solvable nonlinear equations : proceedings of the Conference on Nonlinear Evolution Equations, Solitons and the Inverse Scattering Transform, Oberwolfach, Germany, July 27-August 2, 1986 (1987) (73)
The Korteweg-de Vries equation and related evolution equations (1974) (72)
An asymptotic approach to the connection problem for the first and the second painlevé equations (1988) (65)
Runaway Electrons in an Ideal Lorentz Plasma (1964) (60)
The Expected Number of Components Under a Random Mapping Function (1954) (50)
A direct proof that solutions of the six Painlevé equations have no movable singularities except poles (1994) (48)
STABILITY OF PLANE MAGNETOHYDRODYNAMIC SHOCKS (1964) (48)
Singularity structure analysis of the continuum Heisenberg spin chain with anisotropy and transverse field: Nonintegrability and chaos (1992) (47)
The Painlevé Connection Problem: An Asymptotic Approach. I (1992) (47)
Application of a Nonlinear WKB Method to the Korteweg–DeVries Equation (1974) (47)
The gyration of a charged particle (1964) (45)
Separating variables in two‐way diffusion equations (1980) (45)
Formulation of the Theory of Turbulence (1968) (39)
On optimal truncation of divergent series solutions of nonlinear differential systems (1999) (38)
Singularity Analysis and its Relation to Complete, Partial and Non-Integrability (1990) (34)
A note on Miura’s transformation (1979) (31)
Asymptotic Theory of the Positive Column of a Gas Discharge (1965) (31)
Hirota Forms for the Six Painlevé Equations from Singularity Analysis (1992) (26)
A ug 2 00 6 On optimal truncation of divergent series solutions of nonlinear differential systems ; Berry smoothing (2003) (22)
First Correction to the Second Adiabatic Invariant of Charged‐Particle Motion (1966) (22)
Optimal Uniform Estimates and Rigorous Asymptotics Beyond all Orders for a Class of Ordinary Differential Equations ∗ (1996) (20)
Connection Results for the First Painlevé Equation (1992) (16)
Flexibility in Applying the Painlevé Test (1992) (16)
Calculus of variations and supplementary notes and exercises, 1945-1946 (1956) (16)
Optical uniform estimates and rigorous asymptotics beyond all orders for a class of ordinary differential equations (1996) (15)
Equilibrium and Stability of Helical Hydromagnetic Systems (1962) (14)
Borel summation of adiabatic invariants (2004) (13)
Exact Invariants for a Class of Nonlinear Wave Equations (1966) (13)
Note on solutions to a class of nonlinear singular integro-differential equations (1987) (13)
A Local Asymptotic Method of Seeing the Natural Barrier of the Solutions of the Chazy Equation (1993) (12)
The bridge theorem for minimal surfaces (1954) (11)
Nonintegrability criteria for a class of differential equations with two regular singular points (2003) (10)
Analyzable Functions and Applications (2005) (10)
Analytic methods for obstruction to integrability in discrete dynamical systems (2005) (9)
Reflection coefficient beyond all orders for singular problems. II: Closed‐spaced critical points on the nearest critical level line (1991) (7)
Movable Singularities of Solutions of Difference Equations in Relation to Solvability and a Study of a Superstable Fixed Point (2002) (7)
Reflection Coefficient Beyond All Orders for Singular Problems (1991) (7)
Introduction to surreal numbers (1987) (5)
A Multiple-Bounce Theory for the Expansion and Retardation of a Cold-Plasma Explosion Bubble. (1965) (5)
Some Constants of the Linearized Motion of Vlasov Plasmas (1965) (5)
Theory of Turbulence (1966) (5)
ENTROPY PRINCIPLE FOR THE DERIVATION OF A NEW CLUSTER EXPANSION. (1970) (5)
An ODE to a PDE: Glories of the KdV equation. An appreciation of the equation on its 100th birthday! (1995) (4)
Erratum: Asymptotic Theory of the Positive Column of a Gas Discharge (1966) (4)
“Completeness” of the Painlevé Test—General Considerations—Open Problems (1999) (4)
Three Lessons on the Painlevé Property and the Painlevé Equations (2004) (3)
An instability due to the local mixing-length approximation. (1977) (3)
PROPERTY OF LARGE-AMPLITUDE STEADY ELECTROSTATIC WAVES. (1969) (3)
Extension of a compact Lorentz manifold (1973) (3)
Advanced theory of gyrating particles (1965) (3)
Erratum: Nonexistence of Small-Amplitude Breather Solutions in φ 4 Theory [Phys. Rev. Lett. 58, 747 (1987)] (1987) (2)
INSTABILITY OF A PINCHED FIELD WITH A LONGITUDINAL MAGNETIC FIELD (1953) (2)
The connection problem for Painlevé transcedents (1986) (2)
Solitons and coherent structures : proceedings of the Conference on Solitons and Coherent Structures held at Santa Barbara, CA, 93106, USA, January 11-16, 1985 (1986) (1)
Optimal uniform estimates and rigorous asymptotics beyond all orders for a class of ODE's (2006) (1)
Reflection coefficient problems for weakly nonlinear wave equations (1992) (0)
Transcendentally small reflection for singular weakly nonlinear problems (1992) (0)
Lyman Spitzer Remembrance Session (1997) (0)
Analyzable functions and applications : International Workshop on Analyzable Functions and Applications, June 17-21, 2002, International Centre for Mathematical Sciences, Edinburgh, Scotland (2005) (0)
"Completeness" of the Painleve Test-General pen Problems (1999) (0)
SHERWOOD REPORT--NO UNCLASSIFIED DISTRIBUTION OR ANNOUNCEMENT UNTIL SEPTEMBER 13, 1958. THE CONDITIONS FOR THE TRANSITION OF MAGNETIC SURFACES BETWEEN HELICAL AND CIRCULAR REGIONS. Technical Memorandum No. 58 (1958) (0)
Movable singularities of solutions of nonlinear differential and difference equations and the Painlevé property (2002) (0)

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