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We consider the nonlinear Schrodinger equation with cubic (focusing or defocusing) nonlinearity on the multidimensional torus.
W. Craig and C. E. Wayne, Periodic solutions of nonlinear Schrödinger equations and the Nash-Moser method , Hamiltonian mechanics (Toruń, 1993), NATO Adv. Sci. Inst. Ser. B Phys., vol. 331, Plenum, New York, 1994, pp. 103–122. MR 1316671 (96d:35129)
1994
Earlier work this paper cites.
J. Bourgain, Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations , Geom. Funct. Anal. 6
1996
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. (2) 143
1996
Earlier work this paper cites.
S. Kuksin, Oscillations in space-periodic nonlinear Schrödinger equations , Geom. Funct. Anal. 7
1997
Earlier work this paper cites.
by same author, Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations , Ann. of Math. (2) 148
1998
Earlier work this paper cites.
D. Bambusi, Birkhoff normal form for some nonlinear PDEs , Comm. Math. Phys. 234
2003
Earlier work this paper cites.
L. van Veen, The quasi-periodic doubling cascade in the transition to weak turbulence , Phys. D 210
2005
Earlier work this paper cites.
D. Bambusi and B. Grébert, Birkhoff normal form for partial differential equations with tame modulus , Duke Math. J. 135
2006
Cited alongside, same era.
C. Cheverry, Cascade of phases in turbulent flows , Bull. Soc. Math. France 134
2006
Cited alongside, same era.
R. Carles, Cascade of phase shifts for nonlinear Schrödinger equations , J. Hyperbolic Differ. Equ. 4
2007
Cited alongside, same era.
B. Grébert, Birkhoff normal form and Hamiltonian PDEs , Partial differential equations and applications, Sémin. Congr., vol. 15, Soc. Math. France, Paris, 2007, pp. 1–46. MR 2352816 (2009d:37130)
2007
Cited alongside, same era.
C. Lubich, On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations , Math. Comp. 77
2008
Cited alongside, same era.
R. Carles, E. Dumas, and C. Sparber, Multiphase weakly nonlinear geometric optics for Schrödinger equations , SIAM J. Math. Anal. 42
2010
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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. 181
2010
Closest in time.
L. H. Eliasson and S. Kuksin, KAM for the nonlinear Schrödinger equation , Ann. Math. 172
2010
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2010
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L. Gauckler and C. Lubich, Nonlinear Schrödinger equations and their spectral semi-discretizations over long times , Found. Comput. Math. 10
2010
Closest in time.
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2009
Cited alongside, same era.
2009
Cited alongside, same era.
E. Faou, Geometric integration of Hamiltonian PDEs and applications to computational quantum mechanics , European Math. Soc., 2011, to appear
2011
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