D-Index & Metrics Best Publications

D-Index & Metrics 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.

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 51 Citations 12,068 136 World Ranking 737 National Ranking 370

Research.com Recognitions

Awards & Achievements

2014 - Fellow of the American Mathematical Society For contributions to existence and stability of solitary waves, and nonlinear dispersive wave propagation.

2010 - SIAM Fellow For contributions to the analysis and applications of nonlinear waves.

1974 - Fellow of John Simon Guggenheim Memorial Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Quantum mechanics
  • Mathematical analysis
  • Geometry

His main research concerns Nonlinear system, Mathematical analysis, Mathematical physics, Classical mechanics and Schrödinger equation. Michael I. Weinstein interconnects Bound state, Hamiltonian, Partial differential equation and Ground state in the investigation of issues within Nonlinear system. His research in Hamiltonian intersects with topics in Dynamical systems theory and Fermi's golden rule.

His research in the fields of Differential equation, Blowing up and Ball overlaps with other disciplines such as Cloaking and Context. His work carried out in the field of Mathematical physics brings together such families of science as Korteweg–de Vries equation, Dispersion and Exponential stability. His studies deal with areas such as Initial value problem, Stability result and Evolution equation as well as Schrödinger equation.

His most cited work include:

  • Nonlinear Schrödinger equations and sharp interpolation estimates (973 citations)
  • Lyapunov stability of ground states of nonlinear dispersive evolution equations (750 citations)
  • Modulational Stability of Ground States of Nonlinear Schrödinger Equations (589 citations)

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

His primary areas of study are Nonlinear system, Quantum mechanics, Mathematical physics, Mathematical analysis and Classical mechanics. His Nonlinear system research incorporates elements of Hamiltonian, Schrödinger equation and Ground state. His work in the fields of Bound state and Bifurcation overlaps with other areas such as Honeycomb structure.

His Mathematical physics study incorporates themes from Periodic function, Lambda, Eigenvalues and eigenvectors and Resolvent. The concepts of his Mathematical analysis study are interwoven with issues in Korteweg–de Vries equation and Exponential stability. The study incorporates disciplines such as Dynamical systems theory, Instability, Quantum, Standing wave and Degenerate energy levels in addition to Classical mechanics.

He most often published in these fields:

  • Nonlinear system (41.00%)
  • Quantum mechanics (36.50%)
  • Mathematical physics (29.00%)

What were the highlights of his more recent work (between 2013-2021)?

  • Quantum mechanics (36.50%)
  • Mathematical physics (29.00%)
  • Dirac operator (7.50%)

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

The scientist’s investigation covers issues in Quantum mechanics, Mathematical physics, Dirac operator, Bound state and Hamiltonian. His work on Nonlinear system, Operator and Semiclassical physics is typically connected to Honeycomb structure as part of general Quantum mechanics study, connecting several disciplines of science. His Nonlinear system research is multidisciplinary, relying on both Continuous spectrum and Lattice.

He has researched Mathematical physics in several fields, including Resolvent, Homogeneous space, Spectral bands, Eigenvalues and eigenvectors and Electronic band structure. In his study, which falls under the umbrella issue of Bound state, Combinatorics is strongly linked to Nonlinear Schrödinger equation. His Hamiltonian research includes elements of Lambda and Schrödinger equation.

Between 2013 and 2021, his most popular works were:

  • A Variational Perspective on Cloaking by Anomalous Localized Resonance (91 citations)
  • Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations (83 citations)
  • Edge States in Honeycomb Structures (46 citations)

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

  • Quantum mechanics
  • Mathematical analysis
  • Electron

Michael I. Weinstein mostly deals with Quantum mechanics, Bound state, Dirac operator, Honeycomb structure and Honeycomb. In general Quantum mechanics study, his work on Eigenvalues and eigenvectors, Operator, Standing wave and Bifurcation analysis often relates to the realm of Operator, thereby connecting several areas of interest. His work carried out in the field of Bound state brings together such families of science as Bifurcation, Schrödinger equation, Dirac, Domain wall and Adiabatic process.

His Schrödinger equation study is concerned with the field of Mathematical analysis as a whole. The various areas that Michael I. Weinstein examines in his Dirac operator study include Classical mechanics, Dirac equation, Hexagonal lattice and Topological insulator. Michael I. Weinstein works mostly in the field of Honeycomb, limiting it down to concerns involving Zigzag and, occasionally, Bifurcation theory.

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

Nonlinear Schrödinger equations and sharp interpolation estimates

Michael I. Weinstein.
Communications in Mathematical Physics (1983)

1623 Citations

Nonlinear Schrödinger equations and sharp interpolation estimates

Michael I. Weinstein.
Communications in Mathematical Physics (1983)

1623 Citations

Lyapunov stability of ground states of nonlinear dispersive evolution equations

Michael I. Weinstein.
Communications on Pure and Applied Mathematics (1986)

939 Citations

Lyapunov stability of ground states of nonlinear dispersive evolution equations

Michael I. Weinstein.
Communications on Pure and Applied Mathematics (1986)

939 Citations

Modulational Stability of Ground States of Nonlinear Schrödinger Equations

Michael I. Weinstein.
Siam Journal on Mathematical Analysis (1985)

869 Citations

Modulational Stability of Ground States of Nonlinear Schrödinger Equations

Michael I. Weinstein.
Siam Journal on Mathematical Analysis (1985)

869 Citations

Eigenvalues, and Instabilities of Solitary Waves

Robert L. Pego;Michael I. Weinstein.
Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences (1992)

540 Citations

Eigenvalues, and Instabilities of Solitary Waves

Robert L. Pego;Michael I. Weinstein.
Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences (1992)

540 Citations

Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation

F. M. Christ;Michael I. Weinstein.
Journal of Functional Analysis (1991)

491 Citations

Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation

F. M. Christ;Michael I. Weinstein.
Journal of Functional Analysis (1991)

491 Citations

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