Fetching the paper…
Reading the bibliography…
We consider the cubic nonlinear Schr\"odinger equation with harmonic trapping on $\mathbb{R}^D$ ($1\leq D\leq 5$).
Semi-classical analysis for the Schrödinger operator and applications, volume 1336 of Lecture Notes in Mathematics
B. Helffer, · 1988
Earlier work this paper cites.
S. Kuksin and J. Pöschel, Invariant Cantor manifolds of quasi periodic oscillations for a nonlinear Schrödinger equation, Ann. of Math
1996
Earlier work this paper cites.
J. Bourgain, Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations, Ann. of Math.,
1998
Earlier work this paper cites.
N. Hayashi and P. Naumkin, Asymptotics for large time of solutions to the nonlinear Schrödinger and Hartree equations. Amer. J. Math
1998
Earlier work this paper cites.
V. Pérez-García, H. Michinel and H. Herrero, Bose-Einstein solitons in highly asymmetric traps, Phys. Rev. A
1998
Earlier work this paper cites.
P. L. Christiansen, M. P. Sorensen and A. C. Scott, Nonlinear Science at the Dawn of the 21st Century
2000
Earlier work this paper cites.
R. Carles, Geometric optics and long range scattering for one-dimensional nonlinear Schrödinger equations. Comm. Math. Phys
2001
Earlier work this paper cites.
J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Global well-posedness for Schrödinger equations with derivative, SIAM J. Math. Anal
2001
Earlier work this paper cites.
Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity
K. Yajima and G. Zhang, · 2004
Earlier work this paper cites.
H. Lindblad and A. Soffer, Scattering and small data completeness for the critical nonlinear Schrödinger equation. Nonlinearity 19 (2006), no. 2, 345–353
2006
Cited alongside, same era.
P. Kevrekidis, D. Frantzeskakis and R. Carretero-Gonzàlez, Emergent nonlinear phenomena in Bose-Einstein condensates, Springer (2008), 398pp
2008
Cited alongside, same era.
R. Carles, Rotating points for the conformal NLS scattering operator, Dynamics of PDE
2009
Cited alongside, same era.
P. Germain, N. Masmoudi and J. Shatah, Global solutions for 3D quadratic Schrödinger equations, Int. Math. Res. Not
2009
Cited alongside, same era.
R. Killip, M. Visan and X. Zhang, Energy-critical NLS with quadratic potential, Comm. Partial Differential Equations
2009
Cited alongside, same era.
D. J. Frantzeskakis, Dark solitons in atomic Bose-Einstein condensates: from theory to experiments, Journal of Physics A Mathematical and Theoretical
2010
Later among the works it cites.
B. Grébert and L. Thomann, KAM for the quantum harmonic oscillator, Comm. Math. Phys
2011
Later among the works it cites.
J. Kato and F. Pusateri, A new proof of long range scattering for critical nonlinear Schrödinger equations, J. Diff. Int. Equ
2011
Later among the works it cites.
Small data scattering for the nonlinear Schrödinger equation on product spaces,
N. Tzvetkov and N. Visciglia, · 2012
Later among the works it cites.
Z. Hani, Long-time strong instability and unbounded orbits for some periodic nonlinear Schödinger equations, Arch. Rat. Mech. Anal
2014
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A pseudoconformal compactification of the nonlinear Schrödinger equation and applications
T. Tao, · 2009
Cited alongside, same era.
J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation. Invent. Math
2010
Cited alongside, same era.
L. H. Eliasson and S. Kuksin, KAM for the nonlinear Schrödinger equation, Ann. of Math
2010
Cited alongside, same era.
Cited in the paper.
Cited in the paper.
P. Germain, Z. Hani and L. Thomann, On the continuous resonant equation for NLS. I. Deterministic analysis, in preparation
Cited in the paper.
P. Germain, Z. Hani and L. Thomann, On the continuous resonant equation for NLS. II. Statistical study, in preparation
Cited in the paper.
Z. Hani and B. Pausader, On scattering for the quintic defocusing nonlinear Schrödinger equation on ℝ × 𝕋 2 \mathbb{R}\times\mathbb{T}^{2} , Comm. Pure and Appl. Math
2014
Closest in time.
Z. Hani, B. Pausader, N. Tzvetkov and N. Visciglia, Growing Sobolev norms for the cubic defocusing Schrödinger equation. Séminaire: Équations aux Dérivées Partielles. 2013–2014, Exp. No. XVI, 11 pp., Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, 2014
2014
Closest in time.
M. Lewin, Limite de champ moyen et condensation de Bose-Einstein, Gazette des Mathématiciens
2014
Closest in time.