Research area
Nonlinear Schrödinger and KleinGordon equations, standing waves, solitons, multisolitons, orbital stability and instability, instability by blowup, variational methods
Grants and awards
 20242028 Local Principal Inverstigator of the ANR Project NQG (National PI Louis Jeanjean)
 20212023 Principal Investigator of the Labex CIMI Project COCASSE
 20202021 Principal Investigator of the CNRS IEA Project Periodic Waves in Nonlinear Dispersive PDE (in collaboration with TaiPeng Tsai in Vancouver)
 20202022 Member of the CIMI Project PDEs on Quantum Graphs (PI Julien Royer)
 20172020 Principal Investigator of the Labex CIMI Project Nonlinear Waves
 20172018 Principal Investigator (french side) of the DutchFrench van Gogh Project NoWaves (François Genoud PI for the Dutch side)
 20142018 Member of the ANR projet MAToS  Mathematical Analysis of Topological Singularities in some physical problems (PI Radu Ignat)
 20142015 Member of the Toulouse Idex Emergence project NewTiTAnS  New Trends in The Analysis of topological Singularities in mathematical physics (PI Radu Ignat)
 20142015 Member of the PHC Amadeus Project "Quantum transport models for semiconductors and BoseEinstein condensates" (PI Claudia Negulescu)
 2011now Prime d'Encadrement Doctoral et de Recherche (formerly Prime d'excellence scientifique)
 20092013 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
 Variational properties of spaceperiodic standing waves of nonlinear Schrödinger equations with general nonlinearities P. Kfoury and S. Le Coz, hal04501704.
 A minimal mass blowup solution on a nonlinear quantum star graph, F. Genoud, S. Le Coz, and J. Royer, hal04045570.
 Computation of excited states for the nonlinear Schrödinger equation: numerical and theoretical analysis C. Besse, R. Duboscq, S. Le Coz, hal04151806.
Software libary
 Grafidi, a Python package for the solution of Partial Differential Equations on complex networks, C. Besse, R. Duboscq, and S. Le Coz.
In journals
 Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation, P. Kfoury, S. Le Coz, and T.P. Tsai, Comptes Rendus Mathématique, 360:867892, 2022. See also the Github repository.
 Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library, C. Besse, R. Duboscq, S. Le Coz, SMAI Journal of Computational Mathematics, 8:147, 2022.
 Gradient Flow Approach to the Calculation of Ground States on Nonlinear Quantum Graphs, C. Besse, R. Duboscq, S. Le Coz, Annales Henri Lebesgue, 5:387428, 2022.
 Stability of the multisolitons of the modified Kortewegde Vries equation, S. Le Coz and Z. Wang, Nonlinearity, 34(10):71097143, 2021.
 Stability of
multisolitons 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 GrossPitaevskii equation,
I. Ianni, S. Le Coz, J. Royer, SIAM J. Math. Anal. 49 (2017), no. 2, 1060–1099

Multispeed 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

Fastmoving 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), 12511282.

Infinite soliton and kinksoliton trains for nonlinear Schrödinger equations, S. Le Coz, T.P. Tsai, Nonlinearity, 27 (2014), 26892709.

Multisolitary waves for the nonlinear KleinGordon equation, J. Bellazzini, M. Ghimenti, and S. Le Coz, Comm. Partial Differential Equations, 39 (2014), no. 8, 1479–1522.

MultiSpeed solitary wave solutions for nonlinear Schrödinger systems, I. Ianni and S. Le Coz, J. London Math. Soc. (2), 89 (2014), 623639.

On the stability of standing waves of KleinGordon equations in a semiclassical regime, M. Ghimenti, S. Le Coz, and M. Squassina, Discrete Contin. Dyn. Syst.  Series A, 33, no 6 (2013), 23892401.

High speed excited multisolitons in nonlinear Schrödinger equations, R. Côte and S. Le Coz, J. Math. Pures Appl. 96 (2011) 135166.

Orbital stability of standing waves of a semiclassical nonlinear SchrödingerPoisson equation, I. Ianni and S. Le Coz, Advances in Differential Equations, 14, (2009), 717748.

Instability for standing waves of nonlinear KleinGordon equations via mountainpass arguments, L. Jeanjean and S. Le Coz, Transactions of the AMS, 361, 10, (2009), 54015416.

A note on BerestyckiCazenave's classical instability result for nonlinear Schrödinger equations, S. Le Coz, Advanced Nonlinear Studies, 8, (2008), 455463.

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), 11031128.
 An existence and stability result for standing waves of nonlinear Schrödinger equations, L. Jeanjean and S. Le Coz, Advances in Differential Equations, 11, (2006), 813840.
Book Chapter
 Standing waves in nonlinear Schrödinger equations, S. Le Coz, Analytical and Numerical Aspects of Partial Differential Equations, de Gruyter, Berlin, (2009), 151192.
Proceedings
 Finite and infinite soliton and kinksoliton 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, multisolitons 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 KleinGordon equations. S. Le Coz, PhD Thesis, University of FrancheComté, 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 14th16th 2011 (with Raphaël Côte and Philippe Gravejat)
Scientific visit
 3 weeks (October 2021) at the University of British Columbia (Vancouver), invited by TaiPeng Tsai.
 2 weeks (October 2019) at the University of British Columbia (Vancouver), invited by TaiPeng 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 (AprilMay 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 TUBerlin 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, RadaMaria 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, TaiPeng (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 BordeauxPauToulouse, 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.
Minicours
 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 CNRSNSFC 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 ParisDauphine, March 2021 (online)
 Online Seminar of Analysis, EPFL, Lausanne, Switzerland, November 2020 (online)
 DGMPPDE 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
 DGMPPDE 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
 DGMPPDE 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 GrossPitaevskii 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 ParisDauphine, France, April 2008
 Séminaire « AnalyseEDP » , 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 AixMarseille I, France, March 2008
 Séminaire d'Analyse, University of CergyPontoise, 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 FrancheComte, 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).
 20132018 Designated member of the "Collège scientifique" Université Paul Sabatier (Mathématiques).
 2016now Elected member of the "souscommission de choix des enseignantschercheurs" IUT A/Université Paul Sabatier (Mathématiques)
 20142018 Member of the Groupe d'Avancement MCF Maths/Info
 20132018 Elected member of the "Collège scientifique" Université Paul Sabatier (Mathématiques).
 20112014 Member of the Web committee of Toulouse Mathematics Institute.
 2016 VicePresident 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 (IUTA).
 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 IUTA Paul Sabatier.
 Google Scholar profile