## Gustafson, Stephen J.

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 Author ID: gustafson.stephen-j Published as: Gustafson, Stephen; Gustafson, S.; Gustafson, Stephen J. more...less Homepage: https://www.math.ubc.ca/~gustaf/ External Links: MGP
 Documents Indexed: 36 Publications since 1997, including 3 Books Co-Authors: 17 Co-Authors with 30 Joint Publications 470 Co-Co-Authors
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### Co-Authors

 5 single-authored 13 Tsai, Tai-Peng 8 Sigal, Israel Michael 6 Nakanishi, Kenji 5 Kang, Kyungkeun 3 Guan, Meijiao 2 Coles, Matt 2 Fröhlich, Jürg Martin 2 Jonsson, B. Lars G. 2 Roxanas, Dimitrios 1 Chang, Shu-Ming 1 Comech, Andrew 1 Inui, Takahisa 1 Le Coz, Stefan 1 Phan, Tuoc Van 1 Shatah, Jalal 1 Ting, Fan 1 Tzaneteas, Tim
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### Serials

 4 Communications in Mathematical Physics 3 Journal of Differential Equations 3 Universitext 2 Communications on Pure and Applied Mathematics 2 IMRN. International Mathematics Research Notices 2 SIAM Journal on Mathematical Analysis 2 Annales Henri Poincaré 1 Journal of Mathematical Physics 1 Nonlinearity 1 Advances in Mathematics 1 Duke Mathematical Journal 1 Journal of Functional Analysis 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of Nonlinear Science 1 Mathematical Research Letters 1 Discrete and Continuous Dynamical Systems 1 Communications in Contemporary Mathematics 1 AMRX. Applied Mathematics Research eXpress 1 SN Partial Differential Equations and Applications
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### Fields

 33 Partial differential equations (35-XX) 13 Statistical mechanics, structure of matter (82-XX) 6 Quantum theory (81-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Fluid mechanics (76-XX) 2 Operator theory (47-XX) 2 Differential geometry (53-XX) 1 Special functions (33-XX) 1 Numerical analysis (65-XX) 1 Classical thermodynamics, heat transfer (80-XX)

### Citations contained in zbMATH Open

32 Publications have been cited 643 times in 472 Documents Cited by Year
Spectra of linearized operators for NLS solitary waves. Zbl 1168.35041
Chang, Shu-Ming; Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2007
Solitary wave dynamics in an external potential. Zbl 1075.35075
Fröhlich, J.; Gustafson, S.; Jonsson, B. L. G.; Sigal, I. M.
2004
Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations. Zbl 1126.35042
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2007
Scattering theory for the Gross-Pitaevskii equation in three dimensions. Zbl 1180.35481
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2009
Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves. Zbl 1072.35167
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2004
Mathematical concepts of quantum mechanics. 2nd ed. Zbl 1333.81002
Gustafson, Stephen J.; Sigal, Israel Michael
2011
Scattering for the Gross-Pitaevskii equation. Zbl 1119.35084
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2006
Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions. Zbl 1375.35485
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2007
Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schrödinger maps on $$\mathbb R^2$$. Zbl 1205.35294
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2010
Long time motion of NLS solitary waves in a confining potential. Zbl 1100.81019
Jonsson, B. Lars G.; Fröhlich, Jürg; Gustafson, Stephen; Sigal, Israel Michael
2006
Schrödinger flow near harmonic maps. Zbl 1144.53085
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2007
Effective dynamics of magnetic vortices. Zbl 1081.35102
Gustafson, S.; Sigal, I. M.
2006
Asymptotic stability of harmonic maps under the Schrödinger flow. Zbl 1170.35091
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2008
The stability of magnetic vortices. Zbl 0955.58015
Gustafson, S.; Sigal, I. M.
2000
Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary. Zbl 1159.35396
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2006
The stability of localized solutions of Landau-Lifshitz equations. Zbl 1028.35059
Gustafson, Stephen; Shatah, Jalal
2002
Statics and dynamics of magnetic vortices and of Nielsen-Olesen (Nambu) strings. Zbl 1417.82033
Gustafson, S.; Sigal, I. M.; Tzaneteas, T.
2010
Mathematical concepts of quantum mechanics. Zbl 1033.81004
Gustafson, Stephen J.; Sigal, Israel Michael
2003
Stability of periodic waves of 1D cubic nonlinear Schrödinger equations. Zbl 1403.35277
Gustafson, Stephen; Le Coz, Stefan; Tsai, Tai-Peng
2017
Global existence and blow-up for harmonic map heat flow. Zbl 1177.35104
Guan, Meijiao; Gustafson, Stephen; Tsai, Tai-Peng
2009
On linear instability of solitary waves for the nonlinear Dirac equation. Zbl 1297.35029
Comech, Andrew; Guan, Meijiao; Gustafson, Stephen
2014
Symmetric solutions of the Ginzburg-Landau equation in all dimensions. Zbl 0883.35041
Gustafson, S.
1997
Dynamic stability of magnetic vortices. Zbl 1010.35007
Gustafson, S.
2002
Stable directions for degenerate excited states of nonlinear Schrödinger equations. Zbl 1230.35129
Gustafson, Stephen; Phan, Tuoc Van
2011
Solitary waves and dynamics for subcritical perturbations of energy critical NLS. Zbl 1462.35350
Coles, Matt; Gustafson, Stephen
2020
Dynamic stability and instability of pinned fundamental vortices. Zbl 1180.35496
Gustafson, S.; Ting, F.
2009
Global, decaying solutions of a focusing energy-critical heat equation in $$\mathbb{R}^4$$. Zbl 1391.35173
Gustafson, Stephen; Roxanas, Dimitrios
2018
Mathematical concepts of quantum mechanics. 3rd edition. Zbl 1451.81002
Gustafson, Stephen J.; Sigal, Israel Michael
2020
A degenerate edge bifurcation in the 1D linearized nonlinear Schrödinger equation. Zbl 1335.35229
Coles, Matt; Gustafson, Stephen
2016
Symmetric solutions of Ginzburg-Landau equations. Zbl 0904.35084
Gustafson, S.
1998
Global questions for map evolution equations. Zbl 1146.35083
Guan, Meijiao; Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2008
Co-rotational chiral magnetic skyrmions near harmonic maps. Zbl 1454.35366
Gustafson, S.; Wang, Li
2021
Co-rotational chiral magnetic skyrmions near harmonic maps. Zbl 1454.35366
Gustafson, S.; Wang, Li
2021
Solitary waves and dynamics for subcritical perturbations of energy critical NLS. Zbl 1462.35350
Coles, Matt; Gustafson, Stephen
2020
Mathematical concepts of quantum mechanics. 3rd edition. Zbl 1451.81002
Gustafson, Stephen J.; Sigal, Israel Michael
2020
Global, decaying solutions of a focusing energy-critical heat equation in $$\mathbb{R}^4$$. Zbl 1391.35173
Gustafson, Stephen; Roxanas, Dimitrios
2018
Stability of periodic waves of 1D cubic nonlinear Schrödinger equations. Zbl 1403.35277
Gustafson, Stephen; Le Coz, Stefan; Tsai, Tai-Peng
2017
A degenerate edge bifurcation in the 1D linearized nonlinear Schrödinger equation. Zbl 1335.35229
Coles, Matt; Gustafson, Stephen
2016
On linear instability of solitary waves for the nonlinear Dirac equation. Zbl 1297.35029
Comech, Andrew; Guan, Meijiao; Gustafson, Stephen
2014
Mathematical concepts of quantum mechanics. 2nd ed. Zbl 1333.81002
Gustafson, Stephen J.; Sigal, Israel Michael
2011
Stable directions for degenerate excited states of nonlinear Schrödinger equations. Zbl 1230.35129
Gustafson, Stephen; Phan, Tuoc Van
2011
Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schrödinger maps on $$\mathbb R^2$$. Zbl 1205.35294
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2010
Statics and dynamics of magnetic vortices and of Nielsen-Olesen (Nambu) strings. Zbl 1417.82033
Gustafson, S.; Sigal, I. M.; Tzaneteas, T.
2010
Scattering theory for the Gross-Pitaevskii equation in three dimensions. Zbl 1180.35481
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2009
Global existence and blow-up for harmonic map heat flow. Zbl 1177.35104
Guan, Meijiao; Gustafson, Stephen; Tsai, Tai-Peng
2009
Dynamic stability and instability of pinned fundamental vortices. Zbl 1180.35496
Gustafson, S.; Ting, F.
2009
Asymptotic stability of harmonic maps under the Schrödinger flow. Zbl 1170.35091
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2008
Global questions for map evolution equations. Zbl 1146.35083
Guan, Meijiao; Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2008
Spectra of linearized operators for NLS solitary waves. Zbl 1168.35041
Chang, Shu-Ming; Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2007
Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations. Zbl 1126.35042
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2007
Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions. Zbl 1375.35485
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2007
Schrödinger flow near harmonic maps. Zbl 1144.53085
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2007
Scattering for the Gross-Pitaevskii equation. Zbl 1119.35084
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2006
Long time motion of NLS solitary waves in a confining potential. Zbl 1100.81019
Jonsson, B. Lars G.; Fröhlich, Jürg; Gustafson, Stephen; Sigal, Israel Michael
2006
Effective dynamics of magnetic vortices. Zbl 1081.35102
Gustafson, S.; Sigal, I. M.
2006
Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary. Zbl 1159.35396
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng
2006
Solitary wave dynamics in an external potential. Zbl 1075.35075
Fröhlich, J.; Gustafson, S.; Jonsson, B. L. G.; Sigal, I. M.
2004
Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves. Zbl 1072.35167
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng
2004
Mathematical concepts of quantum mechanics. Zbl 1033.81004
Gustafson, Stephen J.; Sigal, Israel Michael
2003
The stability of localized solutions of Landau-Lifshitz equations. Zbl 1028.35059
Gustafson, Stephen; Shatah, Jalal
2002
Dynamic stability of magnetic vortices. Zbl 1010.35007
Gustafson, S.
2002
The stability of magnetic vortices. Zbl 0955.58015
Gustafson, S.; Sigal, I. M.
2000
Symmetric solutions of Ginzburg-Landau equations. Zbl 0904.35084
Gustafson, S.
1998
Symmetric solutions of the Ginzburg-Landau equation in all dimensions. Zbl 0883.35041
Gustafson, S.
1997
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### Cited by 531 Authors

 26 Sigal, Israel Michael 16 Cuccagna, Scipio 14 Ionescu, Alexandru D. 14 Raphael, Pierre 13 Wang, Yanqing 12 Maeda, Masaya 11 Gustafson, Stephen J. 9 Wei, Juncheng 8 Martel, Yvan 8 Muñoz, Claudio 8 Tsai, Tai-Peng 8 Yang, Minsuk 7 Holmer, Justin 7 Kang, Kyungkeun 7 Merle, Frank 7 Nakanishi, Kenji 7 Pausader, Benoît 7 Pusateri, Fabio 7 Wu, Gang 6 Bambusi, Dario 6 Comech, Andrew 6 Fröhlich, Jürg Martin 6 Guo, Boling 6 Le Coz, Stefan 6 Squassina, Marco 6 Wang, Youde 5 Boussaid, Nabile 5 Choe, Hi Jun 5 Collot, Charles 5 Dong, Hongjie 5 Germain, Pierre 5 Lenzmann, Enno 5 Li, Gongbao 5 Li, Ze 5 Soffer, Avraham 5 Wolf, Jörg 4 Audiard, Corentin 4 Banica, Valeria 4 Dejak, Steven I. 4 Donninger, Roland 4 Farah, Luiz Gustavo 4 Frank, Rupert L. 4 Gang, Zhou 4 Ghimenti, Marco G. 4 Kowalczyk, Michał 4 Liu, Qiao 4 Marzuola, Jeremy L. 4 Phan, Tuoc Van 4 Roudenko, Svetlana 4 Saut, Jean-Claude 4 Schlag, Wilhelm 4 Spirn, Daniel P. 4 Ting, Fan 4 Vega, Luis 4 Wang, Wendong 4 Xiang, Changlin 4 Yang, Ganshan 4 Zarnescu, Arghir Dani 4 Zhang, Zhifei 4 Zhou, Daoguo 3 Abou-Salem, Walid K. 3 Adami, Riccardo 3 Akahori, Takafumi 3 Bejenaru, Ioan 3 Cacciapuoti, Claudio 3 Chae, Dongho 3 d’Avenia, Pietro 3 de Laire, André 3 de Suzzoni, Anne-Sophie 3 Del Pino, Manuel A. 3 Deng, Qingquan 3 Faupin, Jérémy 3 Georgiev, Vladimir S. 3 Guo, Yan 3 Ibrahim, Slim 3 Jerrard, Robert Leon 3 Jiu, Quansen 3 Jonsson, B. Lars G. 3 Kikuchi, Hiroaki 3 Kim, Jaemyoung 3 Krieger, Joachim 3 Mashkin, Timur 3 Noja, Diego 3 Pelinovsky, Dmitry Efimovich 3 Pisante, Adriano 3 Pu, Xueke 3 Seiringer, Robert 3 Shatah, Jalal 3 Stanislavova, Milena 3 Stefanov, Atanas G. 3 Stuart, David M. A. 3 Sun, Xiaowei 3 Szeftel, Jérémie 3 Tarulli, Mirko 3 Tataru, Daniel 3 Tzaneteas, Tim 3 Wang, Yuexun 3 Yang, Yisong 3 Yao, Xiaohua 3 Yu, Yong ...and 431 more Authors
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### Cited in 127 Serials

 45 Communications in Mathematical Physics 29 Journal of Differential Equations 20 Archive for Rational Mechanics and Analysis 18 Journal of Mathematical Physics 17 SIAM Journal on Mathematical Analysis 17 Discrete and Continuous Dynamical Systems 15 Journal of Mathematical Analysis and Applications 14 Journal of Functional Analysis 11 Physica D 10 Advances in Mathematics 9 Communications in Partial Differential Equations 8 Communications on Pure and Applied Mathematics 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Calculus of Variations and Partial Differential Equations 7 Nonlinearity 6 Mathematische Annalen 6 Transactions of the American Mathematical Society 6 Journal of the European Mathematical Society (JEMS) 6 Annales Henri Poincaré 5 Letters in Mathematical Physics 5 Reviews in Mathematical Physics 5 Inventiones Mathematicae 5 Quarterly of Applied Mathematics 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Journal of Nonlinear Science 5 Journal of Evolution Equations 5 Communications on Pure and Applied Analysis 5 Séminaire Laurent Schwartz. EDP et Applications 4 Applicable Analysis 4 Journal of Statistical Physics 4 NoDEA. Nonlinear Differential Equations and Applications 4 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 3 Journal d’Analyse Mathématique 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Memoirs of the American Mathematical Society 3 Journal of the American Mathematical Society 3 European Journal of Applied Mathematics 3 Journal of Dynamics and Differential Equations 3 Annals of Mathematics. Second Series 3 Acta Mathematica Sinica. English Series 3 Communications in Contemporary Mathematics 3 Science China. Mathematics 2 Mathematical Methods in the Applied Sciences 2 Russian Mathematical Surveys 2 Duke Mathematical Journal 2 Applied Mathematics Letters 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 St. Petersburg Mathematical Journal 2 Journal of Mathematical Fluid Mechanics 2 Nonlinear Analysis. Real World Applications 2 Discrete and Continuous Dynamical Systems. Series B 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Hyperbolic Differential Equations 2 Frontiers of Mathematics in China 2 Discrete and Continuous Dynamical Systems. Series S 2 Advances in Mathematical Physics 2 Bulletin of Mathematical Sciences 2 Annals of PDE 2 Annales Henri Lebesgue 1 Computer Physics Communications 1 Journal of Computational Physics 1 Mathematics of Computation 1 Acta Mathematica 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Indiana University Mathematics Journal 1 Journal of the Mathematical Society of Japan 1 Kodai Mathematical Journal 1 Manuscripta Mathematica 1 Mathematics and Computers in Simulation 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Numerische Mathematik 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Semigroup Forum 1 SIAM Journal on Numerical Analysis 1 Acta Applicandae Mathematicae 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Automated Reasoning 1 International Journal of Mathematics 1 The Journal of Geometric Analysis 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Geometric and Functional Analysis. GAFA 1 Annals of Physics 1 Bulletin of the American Mathematical Society. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 SIAM Journal on Scientific Computing 1 Topological Methods in Nonlinear Analysis 1 Electronic Journal of Differential Equations (EJDE) 1 Advances in Differential Equations 1 Journal of Mathematical Chemistry 1 Mathematical Physics, Analysis and Geometry 1 Taiwanese Journal of Mathematics 1 Regular and Chaotic Dynamics ...and 27 more Serials
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### Cited in 40 Fields

 425 Partial differential equations (35-XX) 101 Fluid mechanics (76-XX) 81 Quantum theory (81-XX) 55 Dynamical systems and ergodic theory (37-XX) 55 Statistical mechanics, structure of matter (82-XX) 26 Global analysis, analysis on manifolds (58-XX) 18 Optics, electromagnetic theory (78-XX) 17 Numerical analysis (65-XX) 16 Operator theory (47-XX) 12 Differential geometry (53-XX) 10 Functional analysis (46-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 6 Ordinary differential equations (34-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Relativity and gravitational theory (83-XX) 5 Measure and integration (28-XX) 5 Biology and other natural sciences (92-XX) 4 Mechanics of particles and systems (70-XX) 4 Mechanics of deformable solids (74-XX) 4 Geophysics (86-XX) 3 Statistics (62-XX) 2 Real functions (26-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)