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- James Colliander

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
34
Citations
6,196
101
World Ranking
2006
National Ranking
82

2003 - Fellow of Alfred P. Sloan Foundation

- Mathematical analysis
- Real number
- Complex number

His main research concerns Mathematical analysis, Nonlinear Schrödinger equation, Nonlinear system, Korteweg–de Vries equation and Schrödinger equation. His Mathematical analysis research is multidisciplinary, incorporating elements of Scattering and Mathematical physics. His studies examine the connections between Scattering and genetics, as well as such issues in Space, with regards to Quintic function.

His study explores the link between Nonlinear Schrödinger equation and topics such as Schrödinger's cat that cross with problems in Hamiltonian and Fourier transform. His studies in Korteweg–de Vries equation integrate themes in fields like Norm, Multilinear map, Breather and Mixed boundary condition. The study incorporates disciplines such as Cauchy problem, Hamiltonian system, Well-posed problem and Gauge theory in addition to Schrödinger equation.

- Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R^3 (430 citations)
- Sharp global well-posedness for KdV and modified KdV on ℝ and (430 citations)
- ASYMPTOTICS, FREQUENCY MODULATION, AND LOW REGULARITY ILL-POSEDNESS FOR CANONICAL DEFOCUSING EQUATIONS (359 citations)

James E. Colliander mostly deals with Mathematical analysis, Nonlinear system, Nonlinear Schrödinger equation, Sobolev space and Schrödinger equation. The concepts of his Mathematical analysis study are interwoven with issues in Korteweg–de Vries equation and Energy. His Nonlinear system research incorporates elements of Conservation law and Scattering.

His Nonlinear Schrödinger equation research includes themes of Hamiltonian and Mathematical physics. His Sobolev space study combines topics in areas such as Arbitrarily large, Schrödinger's cat and Scaling. His work in Schrödinger equation addresses subjects such as Partial differential equation, which are connected to disciplines such as Cauchy problem and Well-posed problem.

- Mathematical analysis (56.25%)
- Nonlinear system (35.71%)
- Nonlinear Schrödinger equation (27.68%)

- Nonlinear Schrödinger equation (27.68%)
- Mathematical analysis (56.25%)
- Nonlinear system (35.71%)

James E. Colliander mainly focuses on Nonlinear Schrödinger equation, Mathematical analysis, Nonlinear system, Sobolev space and Mathematical physics. As a part of the same scientific family, James E. Colliander mostly works in the field of Nonlinear Schrödinger equation, focusing on Initial value problem and, on occasion, Well posedness, Energy and Space. His work on Conservation law as part of general Mathematical analysis research is frequently linked to A priori and a posteriori, thereby connecting diverse disciplines of science.

The Nonlinear system study combines topics in areas such as Norm and Hamiltonian. In his study, Partial differential equation is strongly linked to Quintic function, which falls under the umbrella field of Sobolev space. His Mathematical physics study combines topics from a wide range of disciplines, such as Zakharov system, Upper and lower bounds and Scalar.

- Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation (205 citations)
- Almost sure well-posedness of the cubic nonlinear Schrödinger equation below $L^{2}(\mathbb{T})$ (121 citations)
- Tensor products and correlation estimates with applications to nonlinear Schrödinger equations (86 citations)

- Mathematical analysis
- Real number
- Complex number

His primary scientific interests are in Initial value problem, Mathematical analysis, Nonlinear Schrödinger equation, Well posedness and Nonlinear system. James E. Colliander works mostly in the field of Initial value problem, limiting it down to topics relating to Schrödinger equation and, in certain cases, Conservation law, Direct proof and Tensor product, as a part of the same area of interest. His studies link Mathematical physics with Nonlinear Schrödinger equation.

His work carried out in the field of Mathematical physics brings together such families of science as Space, Energy and Exponential nonlinearity. His study in Well posedness is interdisciplinary in nature, drawing from both Almost surely, Gaussian and Nonlinear smoothing. James E. Colliander has researched Nonlinear system in several fields, including Hamiltonian, Schrödinger's cat, Fourier transform and Sobolev space.

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.

Sharp global well-posedness for KdV and modified KdV on ℝ and

J. Colliander;M. Keel;G. Staffilani;G. Staffilani;H. Takaoka;H. Takaoka.

Journal of the American Mathematical Society **(2003)**

718 Citations

Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R^3

James Colliander;Markus Keel;Gigliola Staffilani;Hideo Takaoka.

Annals of Mathematics **(2008)**

712 Citations

ASYMPTOTICS, FREQUENCY MODULATION, AND LOW REGULARITY ILL-POSEDNESS FOR CANONICAL DEFOCUSING EQUATIONS

Michael Christ;James Colliander;Terrence Tao.

American Journal of Mathematics **(2003)**

439 Citations

Almost Conservation Laws and Global Rough Solutions to a Nonlinear Schrödinger Equation

J. Colliander;M. Keel;G. Staffilani;H. Takaoka.

Mathematical Research Letters **(2002)**

337 Citations

Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation

James Colliander;Markus Keel;Gigiola Staffilani;Hideo Takaoka.

Inventiones Mathematicae **(2010)**

247 Citations

GLOBAL EXISTENCE AND SCATTERING FOR ROUGH SOLUTIONS OF A NONLINEAR SCHR ¨ ODINGER EQUATION ON R 3

J. Colliander;M. Keel;G. Staffilani;H. Takaoka.

Communications on Pure and Applied Mathematics **(2004)**

237 Citations

A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative

James E. Colliander;Markus Keel;Gigliola Staffilani;Hideo Takaoka.

Siam Journal on Mathematical Analysis **(2002)**

224 Citations

Ill-posedness for nonlinear Schrodinger and wave equations

Michael Christ;James Colliander;Terence Tao.

arXiv: Analysis of PDEs **(2003)**

212 Citations

Almost sure well-posedness of the cubic nonlinear Schrödinger equation below $L^{2}(\mathbb{T})$

James Colliander;Tadahiro Oh.

Duke Mathematical Journal **(2012)**

211 Citations

Global well-posedness for Schrödinger equations with derivative

James E. Colliander;Markus Keel;Gigliola Staffilani;Hideo Takaoka.

Siam Journal on Mathematical Analysis **(2001)**

208 Citations

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