Preprints

• Propagation of coherent states in the logarithmic Schrödinger equation.
  With Fangyuan Dong. [preprint]
• Time splitting and error estimates for nonlinear Schrödinger equations with a potential.
  [preprint]

Book

Book chapter

Articles

2025

113. Pathological set with loss of regularity for nonlinear Schrödinger equations.
     With Louise Gassot. Ann. Inst. H. Poincaré C Anal. Non Linéaire 42 (2025), no. 3, pp. 715-753. [article|preprint]
112. On the Cauchy problem for logarithmic fractional Schrödinger equation.
     With Fangyuan Dong. Port. Math. 82 (2025), no. 1/2, pp. 155-175. [article|preprint]

2024

111. Dynamics near the origin of the long range scattering for the one-dimensional Schrödinger equation.
     C. R. Math. Acad. Sci. Paris. 362 (2024), 1717-1742. [article|preprint]
110. Low regularity solutions to the logarithmic Schrödinger equation.
     With Masayuki Hayashi and Tohru Ozawa. Pure Appl. Anal. 6 (2024), no. 3, 859-871. [article|preprint]
109. On nonlinear effects in multiphase WKB analysis for the nonlinear Schrödinger equation.
     Nonlinearity 37 (2024), no. 6, 065017. [article|preprint]
108. Scattering and uniform in time error estimates for splitting method in NLS.
     With Chunmei Su. Found. Comput. Math. 24 (2024), 683-722. [article|preprint]
107. Logarithmic Gross-Pitaevskii equation.
     With Guillaume Ferriere. Comm. Partial Differential Equations 49 (2024), nos. 1-2, 88-120. [article|preprint]

2023

106. On an intercritical log-modified nonlinear Schrödinger equation in two spatial dimensions.
     With Christof Sparber. Proc. Amer. Math. Soc. 151 (2023), no. 10, 4173–4189. [article|preprint]
105. On the Cauchy problem for the Hartree approximation in quantum dynamics.
     With Clotilde Fermanian Kammerer and Caroline Lasser. Nonlinearity 36 (2023), no. 6, 3158-3181. [article|preprint]
104. On stability of rotational 2D binary Bose-Einstein condensates.
     With Van Duong Dinh and Hichem Hajaiej. Ann. Fac. Sci. Toulouse Math. (6) 32 (2023), no. 1, 81-124. [article|preprint]
103. On ground state (in-)stability in multi-dimensional cubic-quintic nonlinear Schrödinger equations.
     With Christian Klein and Christof Sparber. M2AN Math. Model. Numer. Anal. 57 (2023), no. 2, 423-443. [<article|a preprint]
102. On ground states for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.
     With Yavdat Il'yasov. Stud. Appl. Math. 150 (2023), no. 1, 92-118. [article|preprint]
101. Numerical study of the logarithmic Schrödinger equation with repulsive harmonic potential.
     With Chunmei Su. Discrete Contin. Dyn. Syst. Ser. B 28 (2023), no. 5, 3136-3159. [article|preprint]

2022

100. Logarithmic Schrödinger equation and isothermal fluids.
     EMS Surv. Math. Sci. 9 (2022), no. 1, 99-134. [article|preprint]
99. Global weak solutions for quantum isothermal fluids.
    With Kleber Carrapatoso and Matthieu Hillairet. Ann. Inst. Fourier 72 (2022), no. 6, 2241-2298. [article|<preprint]
98. Constructive and destructive interferences in nonlinear hyperbolic equations.
    With Christophe Cheverry. Mém. Soc. Math. Fr. (N.S.) No. 174 (2022), vi+110 pp. [memoir|preprint]
97. Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential.
    With Chunmei Su. Comm. Partial Differential Equations 47 (2022), no. 6, 1176-1192. [article|preprint]
96. Large-time behavior of compressible polytropic fluids and nonlinear Schrödinger equation.
    With Kleber Carrapatoso and Matthieu Hillairet. Quart. Appl. Math. 80 (2022), no. 3, 549-574. [article|preprint]
95. Dynamical approximations for composite quantum systems: Assessment of error estimates for a separable ansatz.
    With Irene Burghardt, Clotilde Fermanian Kammerer, Benjamin Lasorne and Caroline Lasser. J. Phys. A 55 (2022), no. 22, 224010. [article|preprint]
94. Error estimates of local energy regularization for the logarithmic Schrödinger equation.
    With Weizhu Bao, Chunmei Su and Qinglin Tang. Math. Models Methods Appl. Sci. 32, no. 1, 101-136. [article|preprint]

2021

93. Logarithmic Schrödinger equation with quadratic potential.
    With Guillaume Ferriere. Nonlinearity 34 (2021), no. 12, 8283-8310. [article|preprint]
92. Separation of scales: Dynamical approximations for composite quantum systems.
    With Irene Burghardt, Clotilde Fermanian Kammerer, Benjamin Lasorne and Caroline Lasser. J. Phys. A 54 (2021), no. 41, 414002. [article|preprint]
91. Global dynamics below the ground states for NLS under partial harmonic confinement.
    With Alex Ardila. Commun. Math. Sci. 19 (2021), no. 4, 993-1032. [article|preprint]
90. Orbital stability vs. scattering in the cubic-quintic Schrödinger equation.
    With Christof Sparber. Rev. Math. Phys. 33 (2021), no. 3, 2150004. [article|preprint]

2020

89. Norm inflation for nonlinear Schrödinger equations in Fourier-Lebesgue and modulation spaces of negative regularity.
    With Divyang Bhimani. J. Fourier Anal. Appl. 26 (2020), no. 6, 78. [article|preprint]
88. WKB analysis of non-elliptic nonlinear Schrödinger equations.
    With Clément Gallo. Commun. Contemp. Math. 22 (2020), no. 6, 1950045. [article|preprint]
87. A conservation law with spatially localized sublinear damping.
    With Christophe Besse and Sylvain Ervedoza. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 1, 13-50. [article|preprint]

2019

86. Regularized numerical methods for the logarithmic Schrödinger equation.
    With Weizhu Bao, Chunmei Su and Qinglin Tang. Numer. Math. 143 (2019), no. 2, 461-487. [article|preprint]
85. Error estimates of a regularized finite difference method for the logarithmic Schrödinger equation.
    With Weizhu Bao, Chunmei Su and Qinglin Tang. SIAM J. Numer. Anal. 57 (2019), no. 2, 657-680. [article|preprint]

2018

84. Rigidity results in generalized isothermal fluids.
    With Kleber Carrapatoso and Matthieu Hillairet. Annales Henri Lebesgue 1 (2018), 47-85. [article|preprint]
83. Universal dynamics for the defocusing logarithmic Schrödinger equation.
    With Isabelle Gallagher. Duke Math. J. 167 (2018), no. 9, 1761-1801. [article|preprint]

2017

82. Norm-inflation with infinite loss of regularity for periodic NLS equations in negative Sobolev spaces.
    With Thomas Kappeler. Bull. Soc. Math. France 145 (2017), no. 4, 623-642. [article|preprint]
81. Superexponential growth or decay in the heat equation with a logarithmic nonlinearity.
    With Matthieu Alfaro. Dyn. Partial Differ. Equ. 14 (2017), no. 4, 343-358. [article|preprint]
80. Replicator-mutator equations with quadratic fitness.
    With Matthieu Alfaro. Proc. Amer. Math. Soc. 145 (2017), no. 12, 5315-5327. [article|preprint]
79. WKB analysis of generalized derivative nonlinear Schrödinger equations without hyperbolicity.
    With Clément Gallo. Math. Models Methods Appl. Sci. 27 (2017), no. 9, 1727-1742. [article|preprint]
78. On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit II. Analytic regularity.
    With Clément Gallo. Numer. Math. 136 (2017), no. 1, 315-342. [article|preprint]
77. Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective.
    With Anne Nouri. Asymptot. Anal. 102 (2017), 99-117. [article| preprint]

2016

76. On semi-classical limit of nonlinear quantum scattering.
    Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 3, 711-756. [article|preprint]
75. On the spin-1 Bose-Einstein condensates in the presence of Ioffe-Pritchard magnetic field.
    With Hichem Hajaiej. Commun. Contemp. Math. 18 (2016), no. 5, 1550062, 18 pp. [article]

2015

74. Higher order Schrödinger and Hartree-Fock equations.
    With Wolfgang Lucha and Emmanuel Moulay. J. Math. Phys. 56 (2015), no. 12, 122301. [article|preprint]
73. Scattering for the nonlinear Schrödinger equation with a general one-dimensional confinement.
    With Clément Gallo. J. Math. Phys. 56 (2015), no. 10, 101503. [article|preprint]
72. Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential.
    Z. Angew. Math. Phys. 66 (2015), no. 4, 2087-2094. [article|preprint]
71. Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases.
    With Hichem Hajaiej. Bull. Lond. Math. Soc. 47 (2015), no. 3, 509-518. [article|preprint]
70. Finite time extinction for nonlinear Schrödinger equation in 1D and 2D.
    With Tohru Ozawa. Comm. Partial Differential Equations 40 (2015), no. 5, 897-917. [article|preprint]
69. Scattering for nonlinear Schrödinger equation under partial harmonic confinement.
    With Paolo Antonelli and Jorge Drumond Silva. Commun. Math. Phys. 334 (2015), no. 1, 367-396. [article|preprint]
68. On nonlinear Schrödinger type equations with nonlinear damping.
    With Paolo Antonelli and Christof Sparber. Int. Math. Res. Not. 2015 (2015), 740-762. [article| preprint]
67. Large time behavior in nonlinear Schrödinger equation with time dependent potential.
    With Jorge Drumond Silva. Commun. Math. Sci. 13 (2015), no. 2, 443-460. [article|preprint]

2014

66. Explicit solutions for replicator-mutator equations: extinction vs. acceleration.
    With Matthieu Alfaro. SIAM J. Appl. Math. 74 (2014), no. 6, 1919-1934. [article|preprint]
65. On the orbital stability of Gaussian solitary waves in the log-KdV equation.
    With Dmitry Pelinovsky. Nonlinearity 27 (2014), no. 12, 3185-3202. [article|preprint]
64. On the Cauchy problem for Hartree equation in the Wiener algebra.
    With Lounès Mouzaoui. Proc. Amer. Math. Soc. 142 (2014), no. 7, 2469-2482. [article|preprint]
63. Splitting methods for the nonlocal Fowler equation.
    With Afaf Bouharguane. Math. Comp. 83 (2014), no. 287, 1121-1141. [article|preprint]

2013

62. 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]
61. An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit.
    With Christophe Besse and Florian Méhats. Multiscale Model. Simul. 11 (2013), no. 4, 1228-1260. [article|preprint]
60. A nonlinear Landau-Zener formula.
    With Clotilde Fermanian Kammerer. J. Stat. Phys. 152 (2013), no. 4, 619-656. [article|preprint]

2012

59. Nonlinear Schrödinger equation and frequency saturation.
    Anal. PDE 5 (2012), no. 5, 1157-1173. [article|preprint]
58. Geometric optics and instability for NLS and Davey-Stewartson models.
    With Eric Dumas et Christof Sparber. J. Eur. Math. Soc. (JEMS) 14 (2012), no. 6, 1885-1921. [article|preprint]
57. Higher order Schrödinger equations.
    With Emmanuel Moulay. J. Phys. A 45 (2012), no. 39, 395304. [article|preprint]
56. Madelung, Gross-Pitaevskii and Korteweg.
    With Raphaël Danchin and Jean-Claude Saut. Nonlinearity 25 (2012), no. 10, 2843-2873. [article|preprint]
55. Nonlinear dynamics of semiclassical coherent states in periodic potentials.
    With Christof Sparber. J. Phys. A 45 (2012), no. 24, 244032. [article|preprint]
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.
    With 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.
    With 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.
    With 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.
    With 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.
    With Bijan Mohammadi. ESAIM Math. Model. Numer. Anal. 45 (2011), no. 5, 981-1008. [article|preprint]
46. Finite time extinction by nonlinear damping for the Schrödinger equation.
    With Clément Gallo. Comm. Partial Differential Equations 36 (2011), no. 6, 961-975. [article|preprint]
45. Nonlinear Coherent States and Ehrenfest Time for Schrödinger Equations.
    With 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.
    With 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.
    With 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.
    With 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.
    With 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.
    With 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.
    With Isabelle Gallagher. Commun. Math. Phys. 286 (2009), no. 3, 1181-1209. [article|preprint]
37. On the time evolution of Wigner measures for Schrödinger equations.
    With Clotilde Fermanian Kammerer, Norbert Mauser and Hans Peter Stimming. Commun. Pure Appl. Anal. 8 (2009), no. 2, 559-585. [article|preprint]
36. Loss of regularity for supercritical nonlinear Schrödinger equations.
    With Thomas Alazard. Math. Ann. 343 (2009), no. 2, 397-420. [article|preprint]

2008

35. On the Gross-Pitaevskii equation for trapped dipolar quantum gases.
    With Peter A. Markowich et Christof Sparber. Nonlinearity 21 (2008), 2569-2590. [article|preprint]
34. Semiclassical analysis for Hartree equation.
    With Satoshi Masaki. Asymptot. Anal. 58 (2008), no. 4, 211-227. [article|preprint]
33. Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space.
    With Valeria Banica et Gigliola Staffilani. Geom. Funct. Anal. 18 (2008), no. 2, 367-399. [article|preprint]
32. A Poisson formula for the Schrödinger operator.
    With 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.
    With 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.
    With Christophe Besse, Norbert Mauser and 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]
    
27. Numerical aspects of nonlinear Schrödinger equations in the presence of caustics.
    With 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.
    With 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 L²-critical case.
    With 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.
    With Norbert Mauser and 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.
    With 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.
    With Peter A. Markowich and 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.
    With Luc Miller. Osaka J. Math. 41 (2004), no. 3, 693-725. [article|preprint]
15. Focusing of Spherical Nonlinear Pulses in R¹⁺³, III. Sub and Supercritical cases.
    With Jeffrey Rauch. Tohoku Math. J. 56 (2004), no. 3, 393-410. [article|preprint]
14. Nonlinear Schrödinger equations with Stark potential.
    With Yoshihisa Nakamura. Hokkaido Math. J. 33 (2004), no. 3, 719-729. [article|preprint]
13. Focusing of Spherical Nonlinear Pulses in R¹⁺³, II. Nonlinear caustic.
    With Jeffrey Rauch. Rev. Mat. Iberoamericana 20 (2004), no. 3, 815-864. [article]

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.
    With Clotilde Fermanian Kammerer and 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.
    With 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 R¹⁺³.
   With 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]
   
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 R².
   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. [article]