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We consider the cubic defocusing nonlinear Schr\"odinger equation in the two dimensional torus.
On a problem of Poincaré-Birkhoff
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S. Kuksin and J. Pöschel · 1996
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Growth and oscillations of solutions of nonlinear Schrödinger equation
S. Kuksin · 1996
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Long time stability of some small amplitude solutions in nonlinear Schrödinger equations
D. Bambusi · 1997
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On turbulence in nonlinear Schrödinger equations
S. B. Kuksin · 1997
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Oscillations in space-periodic nonlinear Schrödinger equations
S. B. Kuksin · 1997
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On the growth of high sobolev norms of solutions for kdv and schrödinger equations
G. Staffilani · 1997
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Quadratic forms for a 2 2 -D semilinear Schrödinger equation
G. Staffilani · 1997
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Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
J. Bourgain · 1998
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Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations
D. Bambusi · 1999
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Energy cascade for nls on 𝕋 d \mathbb{T}^{d}
R. Carles and Faou E · 2010
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Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation
J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao · 2010
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Bounds on Sobolev norms for the defocusing nonlinear Schrödinger equation on general flat tori
F. Catoire and W.-M. Wang · 2010
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KAM for the nonlinear Schrödinger equation
L. H. Eliasson and S. B. Kuksin · 2010
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P. Gérard and S. Grellier · 2010
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Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations
V. Sohinger · 2010
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Problems in Hamiltonian PDE’s
J. Bourgain · 1999
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Spectral properties of solutions for nonlinear PDEs in the turbulent regime
S. B. Kuksin · 1999
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On diffusion in high-dimensional Hamiltonian systems and PDE
J. Bourgain · 2000
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Bilinear estimates and applications to 2D NLS
J. E. Colliander, J.-M. Delort, C. E. Kenig, and G. Staffilani · 2001
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Birkhoff normal form for some nonlinear PDEs
D. Bambusi · 2003
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KdV & KAM
T. Kappeler and J. Pöschel · 2003
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V. Sohinger · 2010
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Branching of Cantor manifolds of elliptic tori and applications to PDEs
M. Berti and L. Biasco · 2011
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Global and dynamical aspects of nonlinear schrödinger equations on compact manifolds
Z. Hani · 2011
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Arnold diffusion in a pendulum lattice
V. Kaloshin, M. Levi, and M. Saprykina · 2011
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Explicit formula for the solution of the Szegö equation on the real line and applications
O. Pocovnicu · 2011
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Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations on S 1 S^{1}
V. Sohinger · 2011
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J. Colliander, S. Kwon, and T. Oh · 2012
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Normal form theory for the NLS equation
B. Grébert, T. Kappeler, and J. Pöschel · 2012
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First and second order approximations for a nonlinear wave equation
O. Pocovnicu · 2012
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Normal Form for the Schrödinger equation with analytic non–linearities
C. Procesi and M. Procesi · 2012
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