Prépublications

Livre

Semi-classical analysis for nonlinear Schrödinger equations.
World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2008. xii+243 pp. [1er chapitre|bibliographie|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

    2017

  1. 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]
  2. 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]
  3. Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective.
    Avec Anne Nouri. Asymptot. Anal. 102 (2017), 99-117. [preprint]
  4. 2016

  5. On semi-classical limit of nonlinear quantum scattering.
    Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 3, 711-756. [article|preprint]
  6. 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]
  7. 2015

  8. Higher order Schrödinger and Hartree-Fock equations.
    Avec Wolfgang Lucha et Emmanuel Moulay. J. Math. Phys. 56 (2015), no. 12, 122301. [article|preprint]
  9. 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]
  10. Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential.
    Z. Angew. Math. Phys. 66 (2015), no. 4, 2087-2094. [article|preprint]
  11. 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]
  12. 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]
  13. 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]
  14. On nonlinear Schrödinger type equations with nonlinear damping.
    Avec Paolo Antonelli et Christof Sparber. Int. Math. Res. Not. 2015 (2015), 740-762. [article| preprint]
  15. 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]
  16. 2014

  17. Explicit solutions for replicator-mutator equations: extinction vs. acceleration.
    Avec Matthieu Alfaro. SIAM J. Appl. Math. 74 (2014), no. 6, 1919-1934. [article|preprint]
  18. 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]
  19. 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]
  20. Splitting methods for the nonlocal Fowler equation.
    Avec Afaf Bouharguane. Math. Comp. 83 (2014), no. 287, 1121-1141. [article|preprint]
  21. 2013

  22. 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]
  23. 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]
  24. A nonlinear Landau-Zener formula.
    Avec Clotilde Fermanian Kammerer. J. Stat. Phys. 152 (2013), no. 4, 619-656. [article|preprint]
  25. 2012

  26. Nonlinear Schrödinger equation and frequency saturation.
    Anal. PDE 5 (2012), no. 5, 1157-1173. [article|preprint]
  27. 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]
  28. Higher order Schrödinger equations.
    Avec Emmanuel Moulay. J. Phys. A 45 (2012), no. 39, 395304. [article]
  29. Madelung, Gross-Pitaevskii and Korteweg.
    Avec Raphaël Danchin et Jean-Claude Saut. Nonlinearity 25 (2012), no. 10, 2843-2873. [article|preprint]
  30. Nonlinear dynamics of semiclassical coherent states in periodic potentials.
    Avec Christof Sparber. J. Phys. A 45 (2012), no. 24, 244032. [article|preprint]
  31. Interaction of coherent states for Hartree equations.
    Arch. Ration. Mech. Anal. 204 (2012), no. 2, 559-598. [article|preprint]
  32. Energy cascade for NLS on the torus.
    Avec Erwan Faou. Discrete Contin. Dyn. Syst. 32 (2012), no. 6, 2063-2077. [article|preprint]
  33. 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]
  34. 2011

  35. Semiclassical wave packet dynamics for Hartree equations.
    Avec Pei Cao. Rev. Math. Phys. 23 (2011), no. 9, 933-967. [article|preprint]
  36. On Schrödinger equations with modified dispersion.
    Dyn. Partial Differ. Equ. 8 (2011), no. 3, 173-184. [article|preprint]
  37. Nonlinear Schrödinger equation with time dependent potential.
    Commun. Math. Sci. 9 (2011), no. 4, 937-964. [article|preprint]
  38. A Nonlinear Adiabatic Theorem for Coherent States.
    Avec Clotilde Fermanian Kammerer. Nonlinearity 24 (2011), no. 8, 2143-2164. [article|preprint]
  39. 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]
  40. 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]
  41. Nonlinear Coherent States and Ehrenfest Time for Schrödinger Equations.
    Avec Clotilde Fermanian Kammerer. Commun. Math. Phys. 301 (2011), no. 2, 443-472. [article|preprint]
  42. 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]
  43. 2010

  44. 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]
  45. 2009

  46. Supercritical geometric optics for nonlinear Schrödinger equations.
    Avec Thomas Alazard. Arch. Ration. Mech. Anal. 194 (2009), no. 1, 315-347. [article|preprint]
  47. 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]
  48. 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]
  49. Rotating points for the conformal NLS scattering operator.
    Dyn. Partial Differ. Equ. 6 (2009), no. 1, 35-51. [article|preprint]
  50. Analyticity of the scattering operator for semilinear dispersive equations.
    Avec Isabelle Gallagher. Commun. Math. Phys. 286 (2009), no. 3, 1181-1209. [article|preprint]
  51. 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]
  52. Loss of regularity for supercritical nonlinear Schrödinger equations.
    Avec Thomas Alazard. Math. Ann. 343 (2009), no. 2, 397-420. [article|preprint]
  53. 2008

  54. On the Gross-Pitaevskii equation for trapped dipolar quantum gases.
    Avec Peter A. Markowich et Christof Sparber. Nonlinearity 21 (2008), 2569-2590. [article|preprint]
  55. Semiclassical analysis for Hartree equation.
    Avec Satoshi Masaki. Asymptot. Anal. 58 (2008), no. 4, 211-227. [article|preprint]
  56. 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]
  57. A Poisson formula for the Schrödinger operator.
    Avec Tohru Ozawa. J. Fourier Anal. Appl. 14 (2008), no. 3, 475-483. [article|preprint]
  58. 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]
  59. On the wave operators for the critical nonlinear Schrödinger equation.
    Avec Tohru Ozawa. Math. Res. Lett. 15 (2008), no. 1, 185-195. [article|preprint]
  60. 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]
  61. 2007

  62. 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.
  63. 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]
  64. 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]
  65. WKB analysis for nonlinear Schrödinger equations with potential.
    Commun. Math. Phys. 269 (2007), no. 1, 195-221. [article|preprint]
  66. Geometric optics and instability for semi-classical Schrödinger equations.
    Arch. Ration. Mech. Anal. 183 (2007), no. 3, 525-553. [article|preprint]
  67. Cascade of phase shifts for nonlinear Schrödinger equations.
    J. Hyperbolic Differ. Equ. 4 (2007), no. 2, 207-231. [article|preprint]
  68. On the role of quadratic oscillations in nonlinear Schrödinger equations II. The $L^2$-critical case.
    Avec Sahbi Keraani. Trans. Amer. Math. Soc. 359 (2007), no. 1, 33-62. [article|preprint]
  69. 2005

  70. (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]
  71. Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential.
    Commun. Contemp. Math. 7 (2005), no. 4, 483-508. [article|preprint]
  72. Global existence results for nonlinear Schrödinger equations with quadratic potentials.
    Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 385-398. [article|preprint]
  73. 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]
  74. 2004

  75. 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]
  76. Semiclassical nonlinear Schrödinger equations with potential and focusing initial data.
    Avec Luc Miller. Osaka J. Math. 41 (2004), no. 3, 693-725. [article|preprint]
  77. Focusing of Spherical Nonlinear Pulses in $\mathbb R^{1+3}$, III. Sub and Supercritical cases.
    Avec Jeffrey Rauch. Tohoku Math. J. 56 (2004), no. 3, 393-410. [article|preprint]
  78. Nonlinear Schrödinger equations with Stark potential.
    Avec Yoshihisa Nakamura. Hokkaido Math. J. 33 (2004), no. 3, 719-729. [preprint]
  79. Focusing of Spherical Nonlinear Pulses in $\mathbb R^{1+3}$, II. Nonlinear caustic.
    Avec Jeffrey Rauch. Rev. Mat. Iberoamericana 20 (2004), no. 3, 815-864. [article|preprint]
  80. 2003

  81. Nonlinear Schrödinger equations with repulsive harmonic potential and applications.
    SIAM J. Math. Anal. 35 (2003), no. 4, 823-843. [article|preprint]
  82. 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]
  83. 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]
  84. 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]
  85. 2002

  86. Critical nonlinear Schrödinger equations with and without harmonic potential.
    Math. Models Methods Appl. Sci. 12 (2002), no. 10, 1513-1523. [article|preprint]
  87. Remarks on the nonlinear Schrödinger equation with harmonic potential.
    Ann. Henri Poincaré 3 (2002), no. 4, 757-772. [article|preprint]
  88. Focusing of Spherical Nonlinear Pulses in $\mathbb R^{1+3}$.
    Avec Jeffrey Rauch. Proc. Amer. Math. Soc. 130 (2002), 791-804. [article]
  89. 2001

  90. 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.
  91. Geometric Optics and Long Range Scattering for One-Dimensional Nonlinear Schrödinger Equations.
    Commun. Math. Phys. 220 (2001), no. 1, 41-67. [article]
  92. 2000

  93. Focusing on a line for nonlinear Schrödinger equations in $\mathbb R^2$.
    Asymptot. Anal. 24 (2000), 255-276. [article]
  94. Geometric optics with caustic crossing for some nonlinear Schrödinger equations.
    Indiana Univ. Math. Journal 49 (2000), no. 2, 475-551. [article]
  95. 1998

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