Selected publications

Complete list available on Mathscinet.
Recent preprints can be found on Arxiv.

Gross-Pitaevskii equation

• On the Korteweg-de Vries long-wave approximation of the Gross-Pitaevskii equation. I. Int. Math. Res. Not. IMRN 2009, no. 14, 2700--2748,
  with Fabrice Béthuel, Philippe Gravejat, and Jean-Claude Saut.
• Orbital stability of the black soliton for the Gross-Pitaevskii equation. Indiana Univ. Math. J. 57 (2008), no. 6, 2611--2642,
  with Fabrice Béthuel, Philippe Gravejat and Jean-Claude Saut.
• On the NLS dynamics for infinite energy vortex configurations on the plane. Rev. Mat. Iberoam. 24 (2008), no. 2, 671--702,
  with Fabrice Béthuel and Robert L. Jerrard.
• A remark on the Cauchy problem for the 2D Gross-Pitaevskii equation with nonzero degree at infinity. Differential Integral Equations 20 (2007), no. 3, 325--338,
  with Fabrice Béthuel.
• Vortex rings for the Gross-Pitaevskii equation. J. Eur. Math. Soc. (JEMS) 6 (2004), no. 1, 17--94,
  with Fabrice Béthuel and Giandomenico Orlandi.

Parabolic Ginzburg-Landau equation

• Dynamics of multiple degree Ginzburg-Landau vortices. Comm. Math. Phys. 272 (2007), no. 1, 229--261,
  with Fabrice Béthuel and Giandomenico Orlandi.
• Quantization and motion law for Ginzburg-Landau vortices. Arch. Ration. Mech. Anal. 183 (2007), no. 2, 315--370,
  with Fabrice Béthuel and Giandomenico Orlandi.
• Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics. Duke Math. J. 130 (2005), no. 3, 523--614,
  with Fabrice Béthuel and Giandomenico Orlandi.
• Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature. Ann. of Math. (2) 163 (2006), no. 1, 37--163,
  with Fabrice Béthuel and Giandomenico Orlandi.

Euler equations

• Desingularization of Vortices for the Euler Equation. Arch. Ration. Mech. Anal., to appear,
  with Jean Van Schaftingen.

Topological methods and concentration compactness

• Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities. Trans. Amer. Math. Soc. 357 (2005), no. 7, 2909--2938.
• A concentration-compactness lemma with applications to singular eigenvalue problems. J. Funct. Anal. 167 (1999), no. 2, 463--480.

Symmetrization and symmetry breaking

• Partial symmetry and asymptotic behavior for some elliptic variational problems. Calc. Var. Partial Differential Equations 18 (2003), no. 1, 57--75,
  with Michel Willem.
• Non-radial ground states for the Hénon equation. Commun. Contemp. Math. 4 (2002), no. 3, 467--480,
  with Jiabao Su and Michel Willem.

Miscellaneous

• Symmetrization of dissipative-dispersive traveling waves for systems of conservation laws. Phys. D 200 (2005), no. 1-2, 105--123,
  with Fabrice Béthuel and Bruno Despres.
  
• Remarks on a Hardy-Sobolev inequality. C. R. Math. Acad. Sci. Paris 336 (2003), no. 10, 811--815, with Simone Secchi and Michel Willem.
  
• Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations. J. Differential Equations 184 (2002), no. 1, 78--96,
  with Jan Bouwe van den Berg.
• On some infinite sums of integer valued Dirac's masses. C. R. Math. Acad. Sci. Paris 334 (2002), no. 5, 371--374.
  
• Travelling waves for an infinite lattice: multibump type solutions. Topol. Methods Nonlinear Anal. 12 (1998), no. 1, 79--90.
• Solitary waves with prescribed speed on infinite lattices. J. Funct. Anal. 149 (1997), no. 1, 266--275,
  with Michel Willem.