Stefan Le Coz

Research area

Nonlinear Schrödinger and Klein-Gordon equations, standing waves, solitons, multi-solitons, orbital stability and instability, instability by blow-up, variational methods

Grants and awards

• 2021-2023 Principal Investigator of the Labex CIMI Project COCASSE
• 2020-2021 Principal Investigator of the CNRS IEA Project Periodic Waves in Nonlinear Dispersive PDE (in collaboration with Tai-Peng Tsai in Vancouver)
• 2020-2022 Member of the CIMI Project PDEs on Quantum Graphs (PI Julien Royer)
• 2017-2020 Principal Investigator of the Labex CIMI Project Nonlinear Waves
• 2017-2018 Principal Investigator (french side) of the Dutch-French van Gogh Project NoWaves (François Genoud PI for the Dutch side)
• 2014-2018 Member of the ANR projet MAToS - Mathematical Analysis of Topological Singularities in some physical problems (PI Radu Ignat)
• 2014-2015 Member of the Toulouse Idex Emergence project NewTiTAnS - New Trends in The Analysis of topological Singularities in mathematical physics (PI Radu Ignat)
• 2014-2015 Member of the PHC Amadeus Project "Quantum transport models for semiconductors and Bose-Einstein condensates" (PI Claudia Negulescu)
• 2011-now Prime d'Encadrement Doctoral et de Recherche (formerly Prime d'excellence scientifique)
• 2009-2013 Principal Investigator of the ANR project ESONSE - Excited States Of Nonlinear Schrödinger Equations
• 2011 BQR AO4 nouvel arrivant de l'université Paul Sabatier

Publications

Preprints

• Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library, C. Besse, R. Duboscq, S. Le Coz, hal-03164639.
• Stability of the multi-solitons of the modified Korteweg-de Vries equation, S. Le Coz, Z. Wang, arXiv:2010.00814.
• Gradient Flow Approach to the Calculation of Ground States on Nonlinear Quantum Graphs, C. Besse, R. Duboscq, S. Le Coz, arXiv:2006.04404.

In journals

• Stability of multi-solitons for the derivative nonlinear Schrödinger equation, S. Le Coz, Y. Wu, Int. Math. Res. Notices (2018), no. 13, 4120–4170
  
• Stability of Periodic Waves of 1D Cubic Nonlinear Schrödinger Equations , S. Gustafson, S. Le Coz, T.-P. Tsai, Appl. Math. Res. Express (2017), no. 2, 431–487
  
• On the Cauchy problem and the black solitons of a singularly perturbed Gross-Pitaevskii equation, I. Ianni, S. Le Coz, J. Royer, SIAM J. Math. Anal. 49 (2017), no. 2, 1060–1099
  
• Multi-speed solitary waves of nonlinear Schrödinger systems: theoretical and numerical analysis, F. Delebecque, S. Le Coz, R.-M. Weishäupl, Commun. Math. Sci. 14 (2016), no. 6, 1599–1624.
  
• Minimal mass blow up solutions for a double power nonlinear Schrödinger equation, S. Le Coz, Y. Martel, and P. Raphael, Rev. Mat. Iberoam. 32 (2016), no. 3, 795–833
  
• Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations, S. Le Coz, D. Li, T.-P. Tsai, Proc. Roy. Soc. Edinburgh Sect. A, 145 (2015), 1251-1282.
  
• Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations, S. Le Coz, T.-P. Tsai, Nonlinearity, 27 (2014), 2689-2709.
  
• Multi-solitary waves for the nonlinear Klein-Gordon equation, J. Bellazzini, M. Ghimenti, and S. Le Coz, Comm. Partial Differential Equations, 39 (2014), no. 8, 1479–1522.
  
• Multi-Speed solitary wave solutions for nonlinear Schrödinger systems, I. Ianni and S. Le Coz, J. London Math. Soc. (2), 89 (2014), 623-639.
  
• On the stability of standing waves of Klein-Gordon equations in a semiclassical regime, M. Ghimenti, S. Le Coz, and M. Squassina, Discrete Contin. Dyn. Syst. - Series A, 33, no 6 (2013), 2389-2401.
  
• High speed excited multi-solitons in nonlinear Schrödinger equations, R. Côte and S. Le Coz, J. Math. Pures Appl. 96 (2011) 135-166.
  
• Orbital stability of standing waves of a semi-classical nonlinear Schrödinger-Poisson equation, I. Ianni and S. Le Coz, Advances in Differential Equations, 14, (2009), 717-748.
  
• Instability for standing waves of nonlinear Klein-Gordon equations via mountain-pass arguments, L. Jeanjean and S. Le Coz, Transactions of the AMS, 361, 10, (2009), 5401-5416.
  
• A note on Berestycki-Cazenave's classical instability result for nonlinear Schrödinger equations, S. Le Coz, Advanced Nonlinear Studies, 8, (2008), 455-463.
  
• Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential, S. Le Coz, R. Fukuizumi, G. Fibich, B. Ksherim and Y. Sivan, Physica D, 237, (2008), 1103-1128.
  
• An existence and stability result for standing waves of nonlinear Schrödinger equations, L. Jeanjean and S. Le Coz, Advances in Differential Equations, 11, (2006), 813-840.

Book Chapter

• Standing waves in nonlinear Schrödinger equations, S. Le Coz, Analytical and Numerical Aspects of Partial Differential Equations, de Gruyter, Berlin, (2009), 151-192.

Proceedings

• Finite and infinite soliton and kink-soliton trains of nonlinear Schrödinger equations, S. Le Coz, T.-P. Tsai, Proceedings of the 6th International Congress of Chinese Mathematicians, Advanced Lectures in Mathematics, Volume 36, International Press, (2017), pp. 43–56.

Dissertations

• Existence et stabilité de solitons, multi-solitons et solutions explosives dans quelques équations dispersives non linéaires. S. Le Coz, Accreditation to Supervise Research (HDR), Université Toulouse 3, 2018.
• Existence, stability and instability of standing waves for nonlinear Schrödinger and Klein-Gordon equations. S. Le Coz, PhD Thesis, University of Franche-Comté, 2007.

Workshop organisation

• Nonlinear Waveguides and Related Topics, October 2018, Toulouse, France (with Julien Royer)
• Analysis of singular patterns in variational models, June 2018, Toulouse, France (with Radu Ignat and Mihai Maris)
• Second Meeting of the ANR Project MAToS, December 12th and 13th, 2016, Toulouse, France (with Radu Ignat)
• Special Session Nonlinear waves in dispersive equations at the 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 1st to 5th, 2016, Orlando, Florida, USA (with François Genoud)
• Analytical and Numerical Advances Around Schrödinger Equations, Toulouse, October 22th to 26th, 2012 (with Rémi Carles, Fanny Delebecque and Claudia Negulescu)
• Workshop "Nonlinear PDE day", Toulouse, May 30th, 2012
• Journée Schrödinger, Toulouse, January 27th 2012 (with Claudia Negulescu).
• Conference "Nonlinear Dispersive PDE & related topics", Paris, June 14th-16th 2011 (with Raphaël Côte and Philippe Gravejat)

Scientific visit

• 3 weeks (October 2021) at the University of British Columbia (Vancouver), invited by Tai-Peng Tsai.
• 2 weeks (October 2019) at the University of British Columbia (Vancouver), invited by Tai-Peng Tsai.
• 1 week (November 2018) at TU Delft (Delft), invited by Anna Geyer in the framework of the PHC Van Gogh project Nonlinear Waveguides.
• 1 week (November 2016) at TU Delft (Delft), invited by François Genoud.
• 1 week (October 2016) at the IAPCM (Beijing), invited by Changxing Miao.
• 1 week (January 2016) at Tokyo University of Science (Tokyo), invited by Masahito Ohta.
• 1 week (August 2014) at the IAPCM (Beijing), invited by Changxing Miao.
• 1 week (October 2013) at the IAPCM (Beijing), invited by Changxing Miao.
• 6 weeks (April-May 2012) at the University of British Columbia (Vancouver), invited by Tai Peng Tsai.
• 1 week (February 2012) at the University of Roma, invited by Isabella Ianni.
• 1 week (January 2012) at the University of Pisa, invited by Marco Ghimenti.
• 1 week (March 2009) at the University of Verona, invited by Marco Squassina.
• 2 weeks in Japan (January 2008) at the University of Kyoto and University of Saitama, invited by Masahito Ohta and Yoshio Tsutsumi.
• 4 weeks (December 2007 and January 2008) at the TU-Berlin in the team of Petra Wittbold.
• 6 months (from January to June 2007) at the Mathematical Institute of the JLU Giessen in the team of Thomas Bartsch.

Invitation of researchers

• November 2021, Stephen Gustafson, University of British Columbia, (1 month)
• June 2018 to May 2019, Zhong Wang, Foshan University, (1 year)
• September 2017, Yifei Wu, Tianjin University, (1 month)
• May 2016, François Genoud, Delft University of Technology, (1 month)
• October 2015, Stephen Gustafson, University of British Columbia, (2 weeks)
• October 2013, Jacopo Bellazzini, University of Sassari, (1 week)
• September 2013, Rada-Maria Weishäupl, University of Vienna, (1 week)
• April 2013, Isabella Ianni, University of Naples II, (1 month)
• October 2012, Jacopo Bellazzini, University of Sassari, (1 week)
• May 2012, Marco Ghimenti, University of Pisa, (1 week)
• December 2011, Isabella Ianni, University of Naples II, (1 week)
• June 2010, Alessandro Selvitella, SISSA, (2 weeks)
• May 2010, Marco Ghimenti, University of Pisa, (2 weeks)

Collaborators

• Bellazzini, Jacopo (Italy)
• Besse, Christophe (France - Toulouse)
• Côte, Raphaël (France - Paris)
• Delebecque, Fanny (France - Toulouse)
• Duboscq, Romain (France - Toulouse)
• Fibich, Gadi (Israël)
• Fukuizumi, Reika (Japon)
• Ghimenti, Marco (Italy)
• Gustafson, Stephen (Canada)
• Ianni, Isabella (Italy)
• Jeanjean, Louis (France - Besançon)
• Ksherim, Baruch (Israël)
• Li, Dong (Canada)
• Martel, Yvan (France - Paris)
• Raphaël, Pierre (France - Nice)
• Royer, Julien (France - Toulouse)
• Sivan, Yonatan (Israël)
• Squassina, Marco (Italy)
• Tsai, Tai-Peng (Canada)
• Wang, Zhong (China)
• Weishäupl, Rada Maria (Austria)
• Wu, Yifei (China)

Communications

Workshop

• 2020 Conference on PDE and dynamical systems, Foshan, China (online), November 2020
• CIMI en fête, Toulouse, France, November 2019
• Nonlinear phenomena in dispersive equations, Lille, France, June 2018
• Intensive week of PDEs, Spa, Belgium, December 2017
• Mathematical Congress of the Americas, Montreal, Canada, July 2017
• Second Meeting of the ANR MAToS, Toulouse, France, December, 2016
• The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, USA, July, 2016
• Quantum Vortices and Nonlinear Waves 2016, Tokyo, Japan, January, 2016
• Quasilinear and nonlocal nonlinear Schrödinger equations, Vienna, Austria, October, 2015
• Workshop in Nonlinear PDEs, Brussels, Belgium, September 7–11, 2015
• Modelling and Numerics for Quantum Systems, Toulouse, France, September, 2015
• The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain, July, 2014
• Journées Bordeaux-Pau-Toulouse, Anglet, France, September 2013.
• Regimes asymptotiques pour l'equation de Schrodinger non linéaire, CIRM Marseille, France, September 2012.
• Stability problems in nonlinear dispersive PDEs , Cergy,France, November 2011.
• « Dynamique des ondes non linéaires », Toulouse, France, December 2010.
• Journées John Ball, Paris, March 2010.
• 4^th meeting of the GDR MOAD, Lyon, France, March 2008.
• « Nonlinear Wave and Dispersive Equations », Kyoto, Japan, January 2008.

Mini-cours

• 5 hours on « Multisolitons of NLS » during the Spring school on nonlinear PDEs, Roma, Italy, March 2014.
• 2 hours on « Multisolitons of NLS » during the CNRS-NSFC Joint Sino- French Summer Institute Dynamics of nonlinear dispersive and fluid mechanics equations, Beijing, China, July 2012. (link here to the slides of the course)
• 6 hours on « Orbital stability for standing waves of nonlinear Schrödinger equations » for graduate student at SISSA, Trieste, Italy, February and March 2008.
• 6 hours on « Standing waves in nonlinear Schrödinger equations » for graduate student at the TU Berlin, Germany, December 2007 and January 2008.

Local Talks

• Séminaire d'Analyse et Probabilités de Paris-Dauphine, March 2021 (online)
• Online Seminar of Analysis, EPFL, Lausanne, Switzerland, November 2020 (online)
• DG-MP-PDE Seminar, UBC, Vancouver, Canada, October, 2019
• Séminaire EDP, Nancy, November 2018
• Analysis Seminar, TU Delft, Netherlands, November 2018
• Séminaire d'analyse appliquée A ³, Amiens, October 2018
• Colloquium on Analysis and Applications, TU Delft, Netherlands, November 2016
• Seminar IAPCM, Beijing, China, October 2016
• Séminaire d'analyse, Lille, September 2016
• DG-MP-PDE Seminar, UBC, Vancouver, Canada, October, 2014
• Capital Normal University, Beijing, China, August 2014
• Seminar IAPCM, Beijing, China, August 2014
• Capital Normal University, Beijing, China, October 2013
• Seminar IAPCM, Beijing, China, October 2013
• DG-MP-PDE Seminar, UBC, Vancouver, Canada, March, 2012
• Seminario Probemi differenziali non lineari, Roma, Italy, February 2012
• Seminar of the Dipartimento di Matematica Applicata, Pisa, Italy, January 2012
• Séminaire ÉDP, Besançon, January 2012
• Séminaire ÉDP, Modélisation et Calcul scientifique, Lyon, April 2011
• Groupe de travail de l'équipe MIP, Toulouse, October 2010
• Séminaire d'analyse appliquée A ³, Amiens, April 2010
• Groupe de travail "Stabilité des solutions des équations de Gross-Pitaevskii et assimilées", December 2009 and January 2010
• Mathematical Seminar, ICTP, Trieste, Italy, March 2009
• Séminaire Analyse Mathématiques et Applications, EPFL, Lausanne, Switzerland, May 2008
• Groupe de travail « Calcul des variations » , University of Paris-Dauphine, France, April 2008
• Séminaire « Analyse-EDP » , University of Toulouse I, France, April 2008
• Groupe de travail « Mécanique des fluides » , University of Toulouse III, France, April 2008
• Séminaire d'Analyse Appliquée, Université of Aix-Marseille I, France, March 2008
• Séminaire d'Analyse, University of Cergy-Pontoise, France, March 2008
• Séminaire de l'Équipe ACSIOM, University of Montpellier II, France, March 2008
• University of Saitama, Tokyo, Japan, January 2008
• University of Waseda, Tokyo, Japan, January 2008
• Kolloquium der Arbeitsgruppe ModNumDiff, TU Berlin, Germany, December 2007
• Kandidatenseminar Analysis, University of Giessen, Germany, January and June 2007
• Séminaire d'Analyse, University of Franche-Comte, France, December 2005 and November 2007

Miscellaneous

• Referee for Advances in Difference Equations, Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, Advances in Differential Equations, Applicable Analysis, Archiv der Mathematik, Asymptotic Analysis, Boletin de la Sociedad Matematica Mexicana Bulletin of the London Mathematical Society, Calculus of Variations and Partial Differential Equations Communications in Contemporary Mathematics, Communications in Mathematical Physics, Communications in Partial Differential Equations Discrete and Continuous Dynamical Systems Series A, Discrete and Continuous Dynamical Systems Series B, European Journal of Applied Mathematics, Evolution Equations and Control Theory (EECT), Funkcialaj Ekvacioj, International Journal of Mathematics and Mathematical Sciences, Journal of Differential Equations, Journal de Mathématiques pues et appliquées (JMPA), Journal of Dynamical and Control Systems, Journal of Dynamics and Differential Equations, Journal of Evolution Equations, Journal of Functional Analysis, Journal of Mathematical Analysis and Applications, Journal of Mathematical Physics, Journal of Physics A: Mathematical and Theoretical, Journal of the European Mathematical Society (JEMS), Math. Control Relat. Fields (MCRF), Matematische Nachrichten, Mathematical Models and Methods in Applied Sciences (M3AS), Nonlinear Analysis Series A: Theory, Methods & Applications, Nonlinearity, Physica D: Nonlinear Phenomena, Proceedings of the Royal Society of Edinburgh, Reviews in Mathematical Physics, Science China Mathematics, SIAM Journal on Mathematical Analysis (SIMA), SN Partial Differential Equations and Applications, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), and Zeitschrift für angewandte Mathematik und Physik (ZAMP).
• 2013-2018 Designated member of the "Collège scientifique" Université Paul Sabatier (Mathématiques).
• 2016-now Elected member of the "sous-commission de choix des enseignants-chercheurs" IUT A/Université Paul Sabatier (Mathématiques)
• 2014-2018 Member of the Groupe d'Avancement MCF Maths/Info
• 2013-2018 Elected member of the "Collège scientifique" Université Paul Sabatier (Mathématiques).
• 2011-2014 Member of the Web committee of Toulouse Mathematics Institute.
• 2016 Vice-President of the Hiring Committee (french Comité de sélection) for the maître de conférence position MCF 26 0470 at University Paul Sabatier.
• 2013 Member of the Hiring Committee (french Comité de sélection) for the maître de conférence position MCF 26 0252 at University Paul Sabatier (IUT-A).
• 2012 Member of the Hiring Committee (french Comité de sélection) for the maître de conférence position MCF 26 0840 at University Paul Sabatier.
• 2012 Member of the Hiring Committee (french Commission de choix) for two ATER positions at IUT-A Paul Sabatier.
• Google Scholar profile