Semiclassical analysis of the nonlinear Schrödinger equation

Book

Book chapter

Articles

• Propagation of coherent states in the logarithmic Schrödinger equation.
  With Fangyuan Dong. [preprint]
• On nonlinear effects in multiphase WKB analysis for the nonlinear Schrödinger equation.
  Nonlinearity 37 (2024), no. 6, 065017. [article|preprint]
• WKB analysis of non-elliptic nonlinear Schrödinger equations.
  With Clément Gallo. Commun. Contemp. Math. 22 (2020), no. 6, 1950045. [article|preprint]
• 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]
• Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective.
  With Anne Nouri. Asymptot. Anal. 102 (2017), 99-117. [article| preprint]
• On semi-classical limit of nonlinear quantum scattering.
  Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 3, 711-756. [article|preprint]
• Geometric optics and instability for NLS and Davey-Stewartson models.
  With Eric Dumas and Christof Sparber. J. Eur. Math. Soc. (JEMS) 14 (2012), no. 6, 1885-1921. [article|preprint]
• Nonlinear dynamics of semiclassical coherent states in periodic potentials.
  With Christof Sparber. J. Phys. A 45 (2012), no. 24, 244032. [article|preprint]
• Interaction of coherent states for Hartree equations.
  Arch. Ration. Mech. Anal. 204 (2012), no. 2, 559-598. [article|preprint]
• 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]
• Semiclassical wave packet dynamics for Hartree equations.
  With Pei Cao. Rev. Math. Phys. 23 (2011), no. 9, 933-967. [article|preprint]
• A Nonlinear Adiabatic Theorem for Coherent States.
  With Clotilde Fermanian Kammerer. Nonlinearity 24 (2011), no. 8, 2143-2164. [article|preprint]
• Nonlinear Coherent States and Ehrenfest Time for Schrödinger Equations.
  With Clotilde Fermanian Kammerer. Commun. Math. Phys. 301 (2011), no. 2, 443-472. [article|preprint]
• Multiphase weakly nonlinear geometric optics for Schrödinger equations.
  With Eric Dumas and Christof Sparber. SIAM J. Math. Anal. 42 (2010), no. 1, 489-518. [article|preprint]
• Supercritical geometric optics for nonlinear Schrödinger equations.
  With Thomas Alazard. Arch. Ration. Mech. Anal. 194 (2009), no. 1, 315-347. [article|preprint]
• 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]
• On the time evolution of Wigner measures for Schrödinger equations.
  With Clotilde Fermanian Kammerer, Norbert Mauser et Hans Peter Stimming. Commun. Pure Appl. Anal. 8 (2009), no. 2, 559-585. [article|preprint]
• Semiclassical analysis for Hartree equation.
  With Satoshi Masaki. Asymptot. Anal. 58 (2008), no. 4, 211-227. [article|preprint]
• 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]
• WKB analysis for nonlinear Schrödinger equations with potential.
  Commun. Math. Phys. 269 (2007), no. 1, 195-221. [article|preprint]
• Geometric optics and instability for semi-classical Schrödinger equations.
  Arch. Ration. Mech. Anal. 183 (2007), no. 3, 525-553. [article|preprint]
• Cascade of phase shifts for nonlinear Schrödinger equations.
  J. Hyperbolic Differ. Equ. 4 (2007), no. 2, 207-231. [article|preprint]
• 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]
• (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]
• 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]
• Semiclassical nonlinear Schrödinger equations with potential and focusing initial data.
  With Luc Miller. Osaka J. Math. 41 (2004), no. 3, 693-725. [article|preprint]
• 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]
• 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]
• Remarques sur les mesures de Wigner.
  C. R. Acad. Sci. Paris, t. 332, Série I, 981-984, 2001. [article]
  
• Geometric Optics and Long Range Scattering for One-Dimensional Nonlinear Schrödinger Equations.
  Commun. Math. Phys. 220 (2001), no. 1, 41-67. [article]
• Focusing on a line for nonlinear Schrödinger equations in R².
  Asymptot. Anal. 24 (2000), 255-276. [article]
• Geometric optics with caustic crossing for some nonlinear Schrödinger equations.
  Indiana Univ. Math. Journal 49 (2000), no. 2, 475-551. [article]