D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 44 Citations 16,383 132 World Ranking 817 National Ranking 56

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Quantum mechanics
  • Partial differential equation

Peter A. Clarkson focuses on Mathematical analysis, Partial differential equation, Differential equation, Mathematical physics and Nonlinear system. The concepts of his Mathematical analysis study are interwoven with issues in Boussinesq approximation and Homogeneous space. His Differential equation research integrates issues from Analytic function, Variety and Singularity.

His Mathematical physics study also includes fields such as

  • Exact solutions in general relativity which connect with Class, Infinitesimal, Heat equation and Differential,
  • Inverse scattering transform together with Dynamical systems theory, Nonlinear evolution and Field. His Nonlinear system research includes elements of Symmetry and Computation. His Inverse scattering problem research is multidisciplinary, incorporating elements of Kadomtsev–Petviashvili equation, Yang–Mills theory and Integrable system.

His most cited work include:

  • Solitons, nonlinear evolution equations and inverse scattering (2994 citations)
  • Solitons, Nonlinear Evolution Equations and Inverse Scattering: References (1128 citations)
  • Solitons, Nonlinear Evolution Equations and Inverse Scattering (832 citations)

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

His primary areas of investigation include Mathematical analysis, Mathematical physics, Nonlinear system, Pure mathematics and Inverse scattering problem. His Mathematical analysis research incorporates themes from Korteweg–de Vries equation and Boussinesq approximation. Peter A. Clarkson has researched Mathematical physics in several fields, including Symmetry, Beta, Homogeneous space, Wave equation and Conservation law.

Peter A. Clarkson works mostly in the field of Nonlinear system, limiting it down to topics relating to Integrable system and, in certain cases, Amplitude, as a part of the same area of interest. His Pure mathematics research incorporates elements of Transformation and Recurrence relation. His work is dedicated to discovering how Inverse scattering problem, Soliton are connected with Theoretical physics and other disciplines.

He most often published in these fields:

  • Mathematical analysis (43.20%)
  • Mathematical physics (39.64%)
  • Nonlinear system (24.26%)

What were the highlights of his more recent work (between 2012-2021)?

  • Orthogonal polynomials (14.20%)
  • Pure mathematics (17.75%)
  • Algebra (11.83%)

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

Orthogonal polynomials, Pure mathematics, Algebra, Nonlinear system and Mathematical physics are his primary areas of study. His Pure mathematics study incorporates themes from Recurrence relation, Order and Order. His work in the fields of Soliton overlaps with other areas such as Constructive.

As part of one scientific family, he deals mainly with the area of Soliton, narrowing it down to issues related to the Conserved quantity, and often Nonlinear Schrödinger equation. His Mathematical physics research incorporates themes from Airy function, Collocation method, Stochastic partial differential equation, Differential equation and Separable partial differential equation. His biological study spans a wide range of topics, including Structure and Rogue wave.

Between 2012 and 2021, his most popular works were:

  • Symmetry Methods for Differential Equations (45 citations)
  • Rational solutions of the Boussinesq equation and applications to rogue waves (38 citations)
  • The relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation (35 citations)

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

  • Mathematical analysis
  • Quantum mechanics
  • Algebra

His primary scientific interests are in Orthogonal polynomials, Pure mathematics, Discrete orthogonal polynomials, Recurrence relation and Laguerre polynomials. His research integrates issues of Mathematical economics and Mathematical society in his study of Orthogonal polynomials. Peter A. Clarkson combines subjects such as Function and Parabolic cylinder function with his study of Recurrence relation.

Peter A. Clarkson studied Parabolic cylinder function and Jacobi polynomials that intersect with Mathematical physics. His Classical orthogonal polynomials study is concerned with Mathematical analysis in general. Peter A. Clarkson interconnects Image and Sigma in the investigation of issues within Mathematical analysis.

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.

Best Publications

Solitons, nonlinear evolution equations and inverse scattering

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

6573 Citations

Solitons, Nonlinear Evolution Equations and Inverse Scattering: References

M. A. Ablowitz;P. A. Clarkson.
(1991)

1828 Citations

New similarity reductions of the Boussinesq equation

Peter A. Clarkson;Martin D. Kruskal.
Journal of Mathematical Physics (1989)

1186 Citations

Symmetry reductions and exact solutions of a class of nonlinear heat equations

Peter A. Clarkson;Peter A. Clarkson;Elizabeth L. Mansfield;Elizabeth L. Mansfield.
Physica D: Nonlinear Phenomena (1994)

388 Citations

The nonclassical method is more general than the direct method for symmetry reductions. An example of the Fitzhugh-Nagumo equation

Maria Clara Nucci;P. A. Clarkson.
Physics Letters A (1992)

274 Citations

Nonclassical symmetry reductions of the Boussinesq equation

Peter A. Clarkson.
Chaos Solitons & Fractals (1995)

217 Citations

Solitary‐Wave Interactions in Elastic Rods

Peter A. Clarkson;Peter A. Clarkson;Randall J. LeVeque;Randall J. LeVeque;Ralph Saxton;Ralph Saxton.
Studies in Applied Mathematics (1986)

188 Citations

New similarity solutions for the modified Boussinesq equation

P A Clarkson.
Journal of Physics A (1989)

175 Citations

Applications of analytic and geometric methods to nonlinear differential equations

P. A Clarkson.
(1993)

158 Citations

Painleve analysis of the non-linear Schrodinger family of equations

P A Clarkson;C M Cosgrove.
Journal of Physics A (1987)

157 Citations

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