Prépublications

• On the Cauchy problem for Hartree equation in the Wiener algebra.
  Avec Lounès Mouzaoui. [preprint]
• Madelung, Gross-Pitaevskii and Korteweg.
  Avec Raphaël Danchin et Jean-Claude Saut. [preprint]
• Splitting methods for the nonlocal Fowler equation.
  Avec Afaf Bouharguane. [preprint]

Livre

Chapitre de livre

Articles

À paraître

• Nonlinear Schrödinger equation and frequency saturation.
  Anal. PDE [preprint]
• Nonlinear dynamics of semiclassical coherent states in periodic potentials.
  Avec Christof Sparber. J. Phys. A [preprint]
• Geometric optics and instability for NLS and Davey-Stewartson models.
  Avec Eric Dumas et Christof Sparber. J. Eur. Math. Soc. (JEMS) [preprint]

2012

54. Interaction of coherent states for Hartree equations.
    Arch. Ration. Mech. Anal. 204 (2012), no. 2, 559-598. [article|preprint]
53. Energy cascade for NLS on the torus.
    Avec Erwan Faou. Discrete Contin. Dyn. Syst. 32 (2012), no. 6, 2063-2077. [article|preprint]
52. 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]

2011

51. Semiclassical wave packet dynamics for Hartree equations.
    Avec Pei Cao. Rev. Math. Phys. 23 (2011), no. 9, 933-967. [article|preprint]
50. On Schrödinger equations with modified dispersion.
    Dyn. Partial Differ. Equ. 8 (2011), no. 3, 173-184. [article|preprint]
49. Nonlinear Schrödinger equation with time dependent potential.
    Commun. Math. Sci. 9 (2011), no. 4, 937-964. [article|preprint]
48. A Nonlinear Adiabatic Theorem for Coherent States.
    Avec Clotilde Fermanian Kammerer. Nonlinearity 24 (2011), no. 8, 2143-2164. [article|preprint]
47. Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime.
    Avec Bijan Mohammadi. M2AN Math. Model. Numer. Anal. 45 (2011), no. 5, 981-1008. [article|preprint]
46. 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]
45. Nonlinear Coherent States and Ehrenfest Time for Schrödinger Equations.
    Avec Clotilde Fermanian Kammerer. Commun. Math. Phys. 301 (2011), no. 2, 443-472. [article|preprint]
44. 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]

2010

43. 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]

2009

42. Supercritical geometric optics for nonlinear Schrödinger equations.
    Avec Thomas Alazard. Arch. Ration. Mech. Anal. 194 (2009), no. 1, 315-347. [article|preprint]
41. 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]
40. 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]
39. Rotating points for the conformal NLS scattering operator.
    Dyn. Partial Differ. Equ. 6 (2009), no. 1, 35-51. [article|preprint]
38. Analyticity of the scattering operator for semilinear dispersive equations.
    Avec Isabelle Gallagher. Commun. Math. Phys. 286 (2009), no. 3, 1181-1209. [article|preprint]
37. 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]
36. Loss of regularity for supercritical nonlinear Schrödinger equations.
    Avec Thomas Alazard. Math. Ann. 343 (2009), no. 2, 397-420. [article|preprint]

2008

35. On the Gross-Pitaevskii equation for trapped dipolar quantum gases.
    Avec Peter A. Markowich et Christof Sparber. Nonlinearity 21 (2008), 2569-2590. [article|preprint]
34. Semiclassical analysis for Hartree equation.
    Avec Satoshi Masaki. Asymptot. Anal. 58 (2008), no. 4, 211-227. [article|preprint]
33. 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]
32. A Poisson formula for the Schrödinger operator.
    Avec Tohru Ozawa. J. Fourier Anal. Appl. 14 (2008), no. 3, 475-483. [article|preprint]
31. 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]
30. On the wave operators for the critical nonlinear Schrödinger equation.
    Avec Tohru Ozawa. Math. Res. Lett. 15 (2008), no. 1, 185-195. [article|preprint]
29. 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]

2007

28. 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.
27. 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]
26. 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]
25. WKB analysis for nonlinear Schrödinger equations with potential.
    Commun. Math. Phys. 269 (2007), no. 1, 195-221. [article|preprint]
24. Geometric optics and instability for semi-classical Schrödinger equations.
    Arch. Ration. Mech. Anal. 183 (2007), no. 3, 525-553. [article|preprint]
23. Cascade of phase shifts for nonlinear Schrödinger equations.
    J. Hyperbolic Differ. Equ. 4 (2007), no. 2, 207-231. [article|preprint]
22. 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]

2005

21. (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]
20. Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential.
    Commun. Contemp. Math. 7 (2005), no. 4, 483-508. [article|preprint]
19. Global existence results for nonlinear Schrödinger equations with quadratic potentials.
    Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 385-398. [article|preprint]
18. 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]

2004

17. 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]
16. Semiclassical nonlinear Schrödinger equations with potential and focusing initial data.
    Avec Luc Miller. Osaka J. Math. 41 (2004), no. 3, 693-725. [article|preprint]
15. 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]
14. Nonlinear Schrödinger equations with Stark potential.
    Avec Yoshihisa Nakamura. Hokkaido Math. J. 33 (2004), no. 3, 719-729. [preprint]
13. 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]

2003

12. Nonlinear Schrödinger equations with repulsive harmonic potential and applications.
    SIAM J. Math. Anal. 35 (2003), no. 4, 823-843. [article|preprint]
11. 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]
10. 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]
9. 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]

2002

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

2001

5. 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.
4. Geometric Optics and Long Range Scattering for One-Dimensional Nonlinear Schrödinger Equations.
   Commun. Math. Phys. 220 (2001), no. 1, 41-67. [article]

2000

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

1998

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