Publications par thème.

Prépublications

Livre

Semi-classical analysis for nonlinear Schrödinger equations - WKB Analysis, Focal Points, Coherent States, 2nd Edition.
World Scientific Publishing Co., Singapore, 2021. xiv+352 pp. [1er chapitre|livre|errata]
1e édition : Semi-classical analysis for nonlinear Schrödinger equations.
World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2008. xii+243 pp. [1er chapitre|livre|errata]

Chapitre de livre

On the semi-classical limit for the nonlinear Schrödinger equation.
Stationary and Time Dependent Gross-Pitaevskii Equations, A. Farina and J.-C. Saut editors, Contemp. Math. 473 (2008), Amer. Math. Soc., pp. 105-127. [preprint]

Articles

    2024

  1. Scattering and uniform in time error estimates for splitting method in NLS.
    Avec Chunmei Su. Found. Comput. Math. 24 (2024), 683-722. [article|preprint]

  2. Logarithmic Gross-Pitaevskii equation.
    Avec Guillaume Ferriere. Comm. Partial Differential Equations 49 (2024), nos. 1-2, 88-120. [article|preprint]

    3. 2023

  3. On an intercritical log-modified nonlinear Schrödinger equation in two spatial dimensions.
    Avec Christof Sparber. Proc. Amer. Math. Soc. 151 (2023), no. 10, 4173–4189. [article|preprint]

  4. On the Cauchy problem for the Hartree approximation in quantum dynamics.
    Avec Clotilde Fermanian Kammerer et Caroline Lasser. Nonlinearity 36 (2023), no. 6, 3158-3181. [article|preprint]

  5. On stability of rotational 2D binary Bose-Einstein condensates.
    Avec Van Duong Dinh et Hichem Hajaiej. Ann. Fac. Sci. Toulouse Math. (6) 32 (2023), no. 1, 81-124. [article|preprint]

  6. On ground state (in-)stability in multi-dimensional cubic-quintic nonlinear Schrödinger equations.
    Avec Christian Klein et Christof Sparber. M2AN Math. Model. Numer. Anal. 57 (2023), no. 2, 423-443. [article|preprint]

  7. On ground states for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.
    Avec Yavdat Il'yasov. Stud. Appl. Math. 150 (2023), no. 1, 92-118. [article|preprint]

  8. Numerical study of the logarithmic Schrödinger equation with repulsive harmonic potential.
    Avec Chunmei Su. Discrete Contin. Dyn. Syst. Ser. B 28 (2023), no. 5, 3136-3159. [article|preprint]

    9. 2022

  9. Logarithmic Schrödinger equation and isothermal fluids.
    EMS Surv. Math. Sci. 9 (2022), no. 1, 99-134. [article|preprint]

  10. Global weak solutions for quantum isothermal fluids.
    Avec Kleber Carrapatoso et Matthieu Hillairet. Ann. Inst. Fourier 72 (2022), no. 6, 2241-2298. [article|preprint]

  11. Constructive and destructive interferences in nonlinear hyperbolic equations.
    Avec Christophe Cheverry. Mém. Soc. Math. Fr. (N.S.) No. 174 (2022), vi+110 pp. [mémoire|preprint]

  12. Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential.
    Avec Chunmei Su. Comm. Partial Differential Equations 47 (2022), no. 6, 1176-1192. [article|preprint]

  13. Large-time behavior of compressible polytropic fluids and nonlinear Schrödinger equation.
    Avec Kleber Carrapatoso et Matthieu Hillairet. Quart. Appl. Math. 80 (2022), no. 3, 549-574. [article|preprint]

  14. Dynamical approximations for composite quantum systems: Assessment of error estimates for a separable ansatz.
    Avec Irene Burghardt, Clotilde Fermanian Kammerer, Benjamin Lasorne et Caroline Lasser. J. Phys. A 55 (2022), no. 22, 224010. [article|preprint]

  15. Error estimates of local energy regularization for the logarithmic Schrödinger equation.
    Avec Weizhu Bao, Chunmei Su et Qinglin Tang. Math. Models Methods Appl. Sci. 32, no. 1, 101-136. [article|preprint]

    16. 2021

  16. Logarithmic Schrödinger equation with quadratic potential.
    Avec Guillaume Ferriere. Nonlinearity 34 (2021), no. 12, 8283-8310. [article|preprint]

  17. Separation of scales: Dynamical approximations for composite quantum systems.
    Avec Irene Burghardt, Clotilde Fermanian Kammerer, Benjamin Lasorne et Caroline Lasser. J. Phys. A 54 (2021), no. 41, 414002. [article|preprint]

  18. Global dynamics below the ground states for NLS under partial harmonic confinement.
    Avec Alex Ardila. Commun. Math. Sci. 19 (2021), no. 4, 993-1032. [article|preprint]

  19. Orbital stability vs. scattering in the cubic-quintic Schrödinger equation.
    Avec Christof Sparber. Rev. Math. Phys. 33 (2021), no. 3, 2150004. [article|preprint]

    20. 2020

  20. Norm inflation for nonlinear Schrödinger equations in Fourier-Lebesgue and modulation spaces of negative regularity.
    Avec Divyang Bhimani. J. Fourier Anal. Appl. 26 (2020), no. 6, 78. [article|preprint]

  21. WKB analysis of non-elliptic nonlinear Schrödinger equations.
    Avec Clément Gallo. Commun. Contemp. Math. 22 (2020), no. 6, 1950045. [article|preprint]

  22. A conservation law with spatially localized sublinear damping.
    Avec Christophe Besse et Sylvain Ervedoza. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 1, 13-50. [article|preprint]

    23. 2019

  23. Regularized numerical methods for the logarithmic Schrödinger equation.
    Avec Weizhu Bao, Chunmei Su et Qinglin Tang. Numer. Math. 143 (2019), no. 2, 461-487. [article|preprint]

  24. Error estimates of a regularized finite difference method for the logarithmic Schrödinger equation.
    Avec Weizhu Bao, Chunmei Su et Qinglin Tang. SIAM J. Numer. Anal. 57 (2019), no. 2, 657-680. [article|preprint]

    25. 2018

  25. Rigidity results in generalized isothermal fluids.
    Avec Kleber Carrapatoso et Matthieu Hillairet. Annales Henri Lebesgue 1 (2018), 47-85. [article|preprint]

  26. Universal dynamics for the defocusing logarithmic Schrödinger equation.
    Avec Isabelle Gallagher. Duke Math. J. 167 (2018), no. 9, 1761-1801. [article|preprint]

    27. 2017

  27. Norm-inflation with infinite loss of regularity for periodic NLS equations in negative Sobolev spaces.
    Avec Thomas Kappeler. Bull. Soc. Math. France 145 (2017), no. 4, 623-642. [article|preprint]

  28. Superexponential growth or decay in the heat equation with a logarithmic nonlinearity.
    Avec Matthieu Alfaro. Dyn. Partial Differ. Equ. 14 (2017), no. 4, 343-358. [article|preprint]

  29. Replicator-mutator equations with quadratic fitness.
    Avec Matthieu Alfaro. Proc. Amer. Math. Soc. 145 (2017), no. 12, 5315-5327. [article|preprint]

  30. WKB analysis of generalized derivative nonlinear Schrödinger equations without hyperbolicity.
    Avec Clément Gallo. Math. Models Methods Appl. Sci. 27 (2017), no. 9, 1727-1742. [article|preprint]

  31. On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit II. Analytic regularity.
    Avec Clément Gallo. Numer. Math. 136 (2017), no. 1, 315-342. [article|preprint]

  32. Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective.
    Avec Anne Nouri. Asymptot. Anal. 102 (2017), 99-117. [article| preprint]

    33. 2016

  33. On semi-classical limit of nonlinear quantum scattering.
    Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 3, 711-756. [article|preprint]

  34. On the spin-1 Bose-Einstein condensates in the presence of Ioffe-Pritchard magnetic field.
    Avec Hichem Hajaiej. Commun. Contemp. Math. 18 (2016), no. 5, 1550062, 18 pp. [article]

    35. 2015

  35. Higher order Schrödinger and Hartree-Fock equations.
    Avec Wolfgang Lucha et Emmanuel Moulay. J. Math. Phys. 56 (2015), no. 12, 122301. [article|preprint]

  36. Scattering for the nonlinear Schrödinger equation with a general one-dimensional confinement.
    Avec Clément Gallo. J. Math. Phys. 56 (2015), no. 10, 101503. [article|preprint]

  37. Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential.
    Z. Angew. Math. Phys. 66 (2015), no. 4, 2087-2094. [article|preprint]

  38. Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases.
    Avec Hichem Hajaiej. Bull. Lond. Math. Soc. 47 (2015), no. 3, 509-518. [article|preprint]

  39. Finite time extinction for nonlinear Schrödinger equation in 1D and 2D.
    Avec Tohru Ozawa. Comm. Partial Differential Equations 40 (2015), no. 5, 897-917. [article|preprint]

  40. Scattering for nonlinear Schrödinger equation under partial harmonic confinement.
    Avec Paolo Antonelli et Jorge Drumond Silva. Commun. Math. Phys. 334 (2015), no. 1, 367-396. [article|preprint]

  41. On nonlinear Schrödinger type equations with nonlinear damping.
    Avec Paolo Antonelli et Christof Sparber. Int. Math. Res. Not. 2015 (2015), 740-762. [article| preprint]

  42. Large time behavior in nonlinear Schrödinger equation with time dependent potential.
    Avec Jorge Drumond Silva. Commun. Math. Sci. 13 (2015), no. 2, 443-460. [article|preprint]

    43. 2014

  43. Explicit solutions for replicator-mutator equations: extinction vs. acceleration.
    Avec Matthieu Alfaro. SIAM J. Appl. Math. 74 (2014), no. 6, 1919-1934. [article|preprint]

  44. On the orbital stability of Gaussian solitary waves in the log-KdV equation.
    Avec Dmitry Pelinovsky. Nonlinearity 27 (2014), no. 12, 3185-3202. [article|preprint]

  45. On the Cauchy problem for Hartree equation in the Wiener algebra.
    Avec Lounès Mouzaoui. Proc. Amer. Math. Soc. 142 (2014), no. 7, 2469-2482. [article|preprint]

  46. Splitting methods for the nonlocal Fowler equation.
    Avec Afaf Bouharguane. Math. Comp. 83 (2014), no. 287, 1121-1141. [article|preprint]

    47. 2013

  47. On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit.
    SIAM J. Numer. Anal. 51 (2013), no. 6, 3232-3258. [article|preprint]

  48. An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit.
    Avec Christophe Besse et Florian Méhats. Multiscale Model. Simul. 11 (2013), no. 4, 1228-1260. [article|preprint]

  49. A nonlinear Landau-Zener formula.
    Avec Clotilde Fermanian Kammerer. J. Stat. Phys. 152 (2013), no. 4, 619-656. [article|preprint]

    50. 2012

  50. Nonlinear Schrödinger equation and frequency saturation.
    Anal. PDE 5 (2012), no. 5, 1157-1173. [article|preprint]

  51. Geometric optics and instability for NLS and Davey-Stewartson models.
    Avec Eric Dumas et Christof Sparber. J. Eur. Math. Soc. (JEMS) 14 (2012), no. 6, 1885-1921. [article|preprint]

  52. Higher order Schrödinger equations.
    Avec Emmanuel Moulay. J. Phys. A 45 (2012), no. 39, 395304. [article|preprint]

  53. Madelung, Gross-Pitaevskii and Korteweg.
    Avec Raphaël Danchin et Jean-Claude Saut. Nonlinearity 25 (2012), no. 10, 2843-2873. [article|preprint]

  54. Nonlinear dynamics of semiclassical coherent states in periodic potentials.
    Avec Christof Sparber. J. Phys. A 45 (2012), no. 24, 244032. [article|preprint]

  55. Interaction of coherent states for Hartree equations.
    Arch. Ration. Mech. Anal. 204 (2012), no. 2, 559-598. [article|preprint]

  56. Energy cascade for NLS on the torus.
    Avec Erwan Faou. Discrete Contin. Dyn. Syst. 32 (2012), no. 6, 2063-2077. [article|preprint]

  57. Semiclassical wave packet dynamics in Schrödinger equations with periodic potentials.
    Avec Christof Sparber. Discrete Contin. Dyn. Syst. Ser. B 17 (2012), no. 3, 759-774. [article|preprint]

    58. 2011

  58. Semiclassical wave packet dynamics for Hartree equations.
    Avec Pei Cao. Rev. Math. Phys. 23 (2011), no. 9, 933-967. [article|preprint]

  59. On Schrödinger equations with modified dispersion.
    Dyn. Partial Differ. Equ. 8 (2011), no. 3, 173-184. [article|preprint]

  60. Nonlinear Schrödinger equation with time dependent potential.
    Commun. Math. Sci. 9 (2011), no. 4, 937-964. [article|preprint]

  61. A Nonlinear Adiabatic Theorem for Coherent States.
    Avec Clotilde Fermanian Kammerer. Nonlinearity 24 (2011), no. 8, 2143-2164. [article|preprint]

  62. Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime.
    Avec Bijan Mohammadi. ESAIM Math. Model. Numer. Anal. 45 (2011), no. 5, 981-1008. [article|preprint]

  63. Finite time extinction by nonlinear damping for the Schrödinger equation.
    Avec Clément Gallo. Comm. Partial Differential Equations 36 (2011), no. 6, 961-975. [article|preprint]

  64. Nonlinear Coherent States and Ehrenfest Time for Schrödinger Equations.
    Avec Clotilde Fermanian Kammerer. Commun. Math. Phys. 301 (2011), no. 2, 443-472. [article|preprint]

  65. Minimal blow-up solutions to the mass-critical inhomogeneous NLS equation.
    Avec Valeria Banica et Thomas Duyckaerts. Comm. Partial Differential Equations 36 (2011), no. 3, 487-531. [article|preprint]

    66. 2010

  66. Multiphase weakly nonlinear geometric optics for Schrödinger equations.
    Avec Eric Dumas et Christof Sparber. SIAM J. Math. Anal. 42 (2010), no. 1, 489-518. [article|preprint]

    67. 2009

  67. Supercritical geometric optics for nonlinear Schrödinger equations.
    Avec Thomas Alazard. Arch. Ration. Mech. Anal. 194 (2009), no. 1, 315-347. [article|preprint]

  68. WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity.
    Avec Thomas Alazard. Ann. Inst. H. Poincaré Anal. Non Linéaire. 26 (2009), no. 3, 959-977. [article|preprint]

  69. On scattering for NLS: from Euclidean to hyperbolic space.
    Avec Valeria Banica et Thomas Duyckaerts. Discrete Contin. Dyn. Syst. 24 (2009), no. 4, 1113-1127. [article|preprint]

  70. Rotating points for the conformal NLS scattering operator.
    Dyn. Partial Differ. Equ. 6 (2009), no. 1, 35-51. [article|preprint]

  71. Analyticity of the scattering operator for semilinear dispersive equations.
    Avec Isabelle Gallagher. Commun. Math. Phys. 286 (2009), no. 3, 1181-1209. [article|preprint]

  72. On the time evolution of Wigner measures for Schrödinger equations.
    Avec Clotilde Fermanian Kammerer, Norbert Mauser et Hans Peter Stimming. Commun. Pure Appl. Anal. 8 (2009), no. 2, 559-585. [article|preprint]

  73. Loss of regularity for supercritical nonlinear Schrödinger equations.
    Avec Thomas Alazard. Math. Ann. 343 (2009), no. 2, 397-420. [article|preprint]

    74. 2008

  74. On the Gross-Pitaevskii equation for trapped dipolar quantum gases.
    Avec Peter A. Markowich et Christof Sparber. Nonlinearity 21 (2008), 2569-2590. [article|preprint]

  75. Semiclassical analysis for Hartree equation.
    Avec Satoshi Masaki. Asymptot. Anal. 58 (2008), no. 4, 211-227. [article|preprint]

  76. Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space.
    Avec Valeria Banica et Gigliola Staffilani. Geom. Funct. Anal. 18 (2008), no. 2, 367-399. [article|preprint]

  77. A Poisson formula for the Schrödinger operator.
    Avec Tohru Ozawa. J. Fourier Anal. Appl. 14 (2008), no. 3, 475-483. [article|preprint]

  78. On the Cauchy problem in Sobolev spaces for nonlinear Schrödinger equations with potential.
    Portugal. Math. (N.S.) 65 (2008), no. 2, 191-209. [article|preprint]

  79. On the wave operators for the critical nonlinear Schrödinger equation.
    Avec Tohru Ozawa. Math. Res. Lett. 15 (2008), no. 1, 185-195. [article|preprint]

  80. Monotonicity properties of blow-up time for nonlinear Schrödinger equation: numerical tests.
    Avec Christophe Besse, Norbert Mauser et Hans Peter Stimming. Discrete Contin. Dyn. Syst. Ser. B 9 (2008), no. 1, 11-36. [article|preprint]

    81. 2007

  81. On instability for the cubic nonlinear Schrödinger equation.
    C. R. Math. Acad. Sci. Paris 344 (2007), no. 8, 483-486. [article|preprint]
    Cette Note est un travail à part entière et ne donnera pas lieu à une publication ultérieure.

  82. Numerical aspects of nonlinear Schrödinger equations in the presence of caustics.
    Avec Laurent Gosse. Math. Models Methods Appl. Sci. 17 (2007), no. 10, 1531-1553. [article|preprint]

  83. Semi-classical limit of Schrödinger-Poisson equations in space dimension n≥3.
    Avec Thomas Alazard. J. Differential Equations 233 (2007), no. 1, 241-275. [article|preprint]

  84. WKB analysis for nonlinear Schrödinger equations with potential.
    Commun. Math. Phys. 269 (2007), no. 1, 195-221. [article|preprint]

  85. Geometric optics and instability for semi-classical Schrödinger equations.
    Arch. Ration. Mech. Anal. 183 (2007), no. 3, 525-553. [article|preprint]

  86. Cascade of phase shifts for nonlinear Schrödinger equations.
    J. Hyperbolic Differ. Equ. 4 (2007), no. 2, 207-231. [article|preprint]

  87. On the role of quadratic oscillations in nonlinear Schrödinger equations II. The L2-critical case.
    Avec Sahbi Keraani. Trans. Amer. Math. Soc. 359 (2007), no. 1, 33-62. [article|preprint]

    88. 2005

  88. (Semi)classical limit of the Hartree equation with harmonic potential.
    Avec Norbert Mauser et Hans Peter Stimming. SIAM J. Appl. Math. 66 (2005), no. 1, 29-56. [article|preprint]

  89. Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential.
    Commun. Contemp. Math. 7 (2005), no. 4, 483-508. [article|preprint]

  90. Global existence results for nonlinear Schrödinger equations with quadratic potentials.
    Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 385-398. [article|preprint]

  91. Scattering theory for the Schrödinger equation with repulsive potential.
    Avec Jean-François Bony, Dietrich Häfner et Laurent Michel. J. Math. Pures Appl. 84 (2005), no. 5, 509-579. [article|preprint]

    92. 2004

  92. Semiclassical asymptotics for weakly nonlinear Bloch waves.
    Avec Peter A. Markowich et Christof Sparber. J. Stat. Phys. 117 (2004), nos. 1-2, 343-375. [article|preprint]

  93. Semiclassical nonlinear Schrödinger equations with potential and focusing initial data.
    Avec Luc Miller. Osaka J. Math. 41 (2004), no. 3, 693-725. [article|preprint]

  94. Focusing of Spherical Nonlinear Pulses in R1+3, III. Sub and Supercritical cases.
    Avec Jeffrey Rauch. Tohoku Math. J. 56 (2004), no. 3, 393-410. [article|preprint]

  95. Nonlinear Schrödinger equations with Stark potential.
    Avec Yoshihisa Nakamura. Hokkaido Math. J. 33 (2004), no. 3, 719-729. [article|preprint]

  96. Focusing of Spherical Nonlinear Pulses in R1+3, II. Nonlinear caustic.
    Avec Jeffrey Rauch. Rev. Mat. Iberoamericana 20 (2004), no. 3, 815-864. [article]

    97. 2003

  97. Nonlinear Schrödinger equations with repulsive harmonic potential and applications.
    SIAM J. Math. Anal. 35 (2003), no. 4, 823-843. [article|preprint]

  98. On the role of quadratic oscillations in nonlinear Schrödinger equations.
    Avec Clotilde Fermanian Kammerer et Isabelle Gallagher. J. Funct. Anal. 203 (2003), no. 2, 453-493. [article|preprint]

  99. Focusing of a pulse with arbitrary phase shift for a nonlinear wave equation.
    Avec David Lannes. Bull. Soc. Math. France 131 (2003), 289-306. [article]

  100. Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation.
    Annales I.H.P., Analyse non linéaire 20 (2003), no. 3, 501-542. [article|preprint]

    101. 2002

  101. Critical nonlinear Schrödinger equations with and without harmonic potential.
    Math. Models Methods Appl. Sci. 12 (2002), no. 10, 1513-1523. [article|preprint]

  102. Remarks on the nonlinear Schrödinger equation with harmonic potential.
    Ann. Henri Poincaré 3 (2002), no. 4, 757-772. [article|preprint]

  103. Focusing of Spherical Nonlinear Pulses in R1+3.
    Avec Jeffrey Rauch. Proc. Amer. Math. Soc. 130 (2002), 791-804. [article]

    104. 2001

  104. Remarques sur les mesures de Wigner.
    C. R. Acad. Sci. Paris, t. 332, Série I, 981-984, 2001. [article]
    Cette Note est un travail à part entière et ne donnera pas lieu à une publication ultérieure.

  105. Geometric Optics and Long Range Scattering for One-Dimensional Nonlinear Schrödinger Equations.
    Commun. Math. Phys. 220 (2001), no. 1, 41-67. [article]

    106. 2000

  106. Focusing on a line for nonlinear Schrödinger equations in R2.
    Asymptot. Anal. 24 (2000), 255-276. [article]

  107. Geometric optics with caustic crossing for some nonlinear Schrödinger equations.
    Indiana Univ. Math. Journal 49 (2000), no. 2, 475-551. [article]

    108. 1998

  108. Comportements précisés près d'une caustique en optique géométrique non linéaire.
    Comm. in Partial Diff. Eq. 23 (1998), nos. 11-12, 1929-1967. [article]