H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 79 Citations 33,660 242 World Ranking 65 National Ranking 37
Engineering and Technology H-index 60 Citations 23,436 194 World Ranking 606 National Ranking 267

Research.com Recognitions

Awards & Achievements

2013 - Fellow of the American Mathematical Society

2011 - SIAM Fellow For contributions to the theory and application of nonlinear waves.

1983 - Fellow of John Simon Guggenheim Memorial Foundation

1975 - Fellow of Alfred P. Sloan Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Quantum mechanics
  • Mathematical analysis
  • Nonlinear system

Mark J. Ablowitz mostly deals with Mathematical analysis, Nonlinear system, Inverse scattering transform, Inverse scattering problem and Mathematical physics. The concepts of his Mathematical analysis study are interwoven with issues in Korteweg–de Vries equation and Soliton. His Nonlinear system research incorporates elements of Separable partial differential equation, Optics, Examples of differential equations and Differential equation.

His biological study spans a wide range of topics, including Split-step method, Nonlinear Schrödinger equation, Fourier transform and Benjamin–Ono equation. His Inverse scattering problem research integrates issues from Initial value problem, Eigenvalues and eigenvectors, Boundary value problem and Scattering theory. As part of the same scientific family, Mark J. Ablowitz usually focuses on Mathematical physics, concentrating on Schrödinger equation and intersecting with Wave equation, Cubic form, Wave packet and Kondratiev wave.

His most cited work include:

  • Solitons and the Inverse Scattering Transform (3015 citations)
  • Solitons, nonlinear evolution equations and inverse scattering (2994 citations)
  • The Inverse scattering transform fourier analysis for nonlinear problems (2328 citations)

What are the main themes of his work throughout his whole career to date?

His scientific interests lie mostly in Nonlinear system, Mathematical analysis, Inverse scattering transform, Soliton and Mathematical physics. The study incorporates disciplines such as Integrable system, Schrödinger's cat, Classical mechanics and Schrödinger equation in addition to Nonlinear system. His work carried out in the field of Classical mechanics brings together such families of science as Amplitude and Nonlinear optics.

In his study, Dispersionless equation is inextricably linked to Korteweg–de Vries equation, which falls within the broad field of Mathematical analysis. His Inverse scattering transform research is multidisciplinary, incorporating perspectives in Initial value problem and Split-step method. His Soliton research is multidisciplinary, relying on both Eigenvalues and eigenvectors, Eigenfunction and Dispersion, Optics.

He most often published in these fields:

  • Nonlinear system (42.32%)
  • Mathematical analysis (42.82%)
  • Inverse scattering transform (20.40%)

What were the highlights of his more recent work (between 2010-2021)?

  • Nonlinear system (42.32%)
  • Mathematical analysis (42.82%)
  • Soliton (19.65%)

In recent papers he was focusing on the following fields of study:

Mark J. Ablowitz spends much of his time researching Nonlinear system, Mathematical analysis, Soliton, Classical mechanics and Mathematical physics. His specific area of interest is Nonlinear system, where Mark J. Ablowitz studies Nonlinear Schrödinger equation. Mark J. Ablowitz has researched Mathematical analysis in several fields, including Korteweg–de Vries equation and Shock wave.

The various areas that Mark J. Ablowitz examines in his Soliton study include Laser and Optics. He combines subjects such as Space and Conservation law with his study of Mathematical physics. Mark J. Ablowitz has included themes like Eigenvalues and eigenvectors and Boundary value problem in his Inverse scattering transform study.

Between 2010 and 2021, his most popular works were:

  • Integrable nonlocal nonlinear Schrödinger equation. (377 citations)
  • Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation (256 citations)
  • Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons (242 citations)

In his most recent research, the most cited papers focused on:

  • Quantum mechanics
  • Mathematical analysis
  • Nonlinear system

Mark J. Ablowitz mainly focuses on Nonlinear system, Mathematical physics, Mathematical analysis, Nonlinear Schrödinger equation and Soliton. His work deals with themes such as Perturbation theory, Edge states, Schrödinger equation, Schrödinger's cat and Classical mechanics, which intersect with Nonlinear system. His Mathematical analysis study integrates concerns from other disciplines, such as Dispersion relation and Shock wave.

Mark J. Ablowitz interconnects Kadomtsev–Petviashvili equation, Dispersionless equation, Nonlinear optics and Inverse scattering transform in the investigation of issues within Nonlinear Schrödinger equation. The study of Inverse scattering transform is intertwined with the study of Korteweg–de Vries equation in a number of ways. His Soliton research focuses on Optics and how it relates to Geometry.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

Solitons, nonlinear evolution equations and inverse scattering

Mark J. Ablowitz;P. A Clarkson.
NASA STI/Recon Technical Report A (1991)

6573 Citations

Solitons and the Inverse Scattering Transform

Mark J. Ablowitz;Harvey Segur.
(1981)

5324 Citations

The Inverse scattering transform fourier analysis for nonlinear problems

Mark J. Ablowitz;David J. Kaup;Alan C. Newell;Harvey Segur.
Studies in Applied Mathematics (1974)

3151 Citations

A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II

M. J. Ablowitz;A. Ramani;H. Segur.
Journal of Mathematical Physics (1980)

1217 Citations

Complex Variables: Introduction and Applications

Mark J. Ablowitz;Athanassios S. Fokas.
(1997)

1123 Citations

Nonlinear-evolution equations of physical significance

Mark J. Ablowitz;David J. Kaup;Alan C. Newell;Harvey Segur.
Physical Review Letters (1973)

1044 Citations

Method for Solving the Sine-Gordon Equation

M. J. Ablowitz;D. J. Kaup;A. C. Newell;H. Segur.
Physical Review Letters (1973)

1021 Citations

Nonlinear differential–difference equations and Fourier analysis

M. J. Ablowitz;J. F. Ladik.
Journal of Mathematical Physics (1976)

955 Citations

Nonlinear differential−difference equations

M. J. Ablowitz;J. F. Ladik.
Journal of Mathematical Physics (1975)

874 Citations

Discrete and continuous nonlinear Schrödinger systems

Mark J. Ablowitz;B. Prinari;A. D. Trubatch.
(2004)

816 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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