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
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 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.
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.
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.
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Solitons, nonlinear evolution equations and inverse scattering
Mark J. Ablowitz;P. A Clarkson.
NASA STI/Recon Technical Report A (1991)
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz;Harvey Segur.
(1981)
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)
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)
Complex Variables: Introduction and Applications
Mark J. Ablowitz;Athanassios S. Fokas.
(1997)
Nonlinear-evolution equations of physical significance
Mark J. Ablowitz;David J. Kaup;Alan C. Newell;Harvey Segur.
Physical Review Letters (1973)
Method for Solving the Sine-Gordon Equation
M. J. Ablowitz;D. J. Kaup;A. C. Newell;H. Segur.
Physical Review Letters (1973)
Nonlinear differential–difference equations and Fourier analysis
M. J. Ablowitz;J. F. Ladik.
Journal of Mathematical Physics (1976)
Nonlinear differential−difference equations
M. J. Ablowitz;J. F. Ladik.
Journal of Mathematical Physics (1975)
Discrete and continuous nonlinear Schrödinger systems
Mark J. Ablowitz;B. Prinari;A. D. Trubatch.
(2004)
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