Nonlinear Schrödinger with potential

• Numerical study of the logarithmic Schrödinger equation with repulsive harmonic potential.
  With Chunmei Su. Discrete Contin. Dyn. Syst. Ser. B [article|preprint]
• 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]
• 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]
• Logarithmic Schrödinger equation with quadratic potential.
  With Guillaume Ferriere. Nonlinearity 34 (2021), no. 12, 8283-8310. [article|preprint]
• 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]
• On semi-classical limit of nonlinear quantum scattering.
  Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 3, 711-756. [article|preprint]
• 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]
• Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential.
  Z. Angew. Math. Phys. 66 (2015), no. 4, 2087-2094. [article|preprint]
• 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]
• 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]
• Nonlinear Schrödinger equation with time dependent potential.
  Commun. Math. Sci. 9 (2011), no. 4, 937-964. [article|preprint]
• 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]
• Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential.
  Commun. Contemp. Math. 7 (2005), no. 4, 483-508. [article|preprint]
• Global existence results for nonlinear Schrödinger equations with quadratic potentials.
  Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 385-398. [article|preprint]
• Nonlinear Schrödinger equations with Stark potential.
  With Yoshihisa Nakamura. Hokkaido Math. J. 33 (2004), no. 3, 719-729. [article|preprint]
• Nonlinear Schrödinger equations with repulsive harmonic potential and applications.
  SIAM J. Math. Anal. 35 (2003), no. 4, 823-843. [article|preprint]
• Critical nonlinear Schrödinger equations with and without harmonic potential.
  Math. Models Methods Appl. Sci. 12 (2002), no. 10, 1513-1523. [article|preprint]
• Remarks on the nonlinear Schrödinger equation with harmonic potential.
  Ann. Henri Poincaré 3 (2002), no. 4, 757-772. [article|preprint]