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We consider the cubic defocusing nonlinear Schr\"odinger equation on the two dimensional torus.
M. Litvak, A transport equation for magneto-hydrodynamic waves , Avco-Everett Res. Rept. 92
1960
Earlier work this paper cites.
K. Hasselmann, On the non-linear energy transfer in a gravity-wave spectrum. I. General theory J. Fluid Mech. 12
1962
Earlier work this paper cites.
V. I. Arnold, Instability of dynamical systems with many degrees of freedom. (Russian) Dokl. Akad. Nauk SSSR 156
1964
Earlier work this paper cites.
D. Benney, P. Saffman, Nonlinear interactions of random waves in a dispersive medium , Proc. Roy. Soc. A 289
1966
Earlier work this paper cites.
V.E. Zakharov, Stability of periodic waves of finite amplitude on a surface of deep fluid , J. Appl. Mech. Tech. Phys. 9
1968
Earlier work this paper cites.
D. Benney and A. Newell, Random wave closures , Stud. Appl. Math. 48
1969
Earlier work this paper cites.
V.E. Zakharov, A.B. Shabat, A. B, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
1971
Earlier work this paper cites.
V. Alekseev, Quasirandom oscillations and qualitative problems in celestial mechanics. (Ninth Mathematical Summer School, Kaciveli, 1971) , Transl. Ser. 2, Am. Math. Soc., 116
1981
Earlier work this paper cites.
R. Douady, P. Le Calvez, Exemple de point fixe elliptique non topologiquement stable en dimension 4 4 , C. R. Acad. Sci. Paris Sér. I Math. 296
1983
Earlier work this paper cites.
O. Kavian, A remark on the blowing-up of solutions of the Cauchy problem for nonlinear Schrödinger equations , Trans. Am. Math. Soc. 299
1987
Earlier work this paper cites.
R. Douady, Stabilité ou instabilité des points fixes elliptiques , Ann. Sci. École Norm. Sup. (4) 21
1988
Earlier work this paper cites.
S. Dyachenko, A.C. Newell, A. C., A. Pushkarev, V.E. Zakharov, Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation
1992
Earlier work this paper cites.
J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations. Geom. Funct. Anal. 3
1993
Earlier work this paper cites.
M. Jordan, Super Bowl XXVII Commercial
1993
Earlier work this paper cites.
J. Bourgain, On the Cauchy problem for periodic KdV-type equations
1995
Earlier work this paper cites.
J. Bourgain, Aspects of long time behaviour of solutions of nonlinear Hamiltonian evolution equations
1995
Earlier work this paper cites.
S. Kuksin, On squeezing and flow of energy for nonlinear wave equations
1995
Earlier work this paper cites.
U. Bessi, An approach to Arnold’s diffusion through the calculus of variations , Nonlinear Anal. 26
1996
Earlier work this paper cites.
J. Bourgain, On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE
1996
Earlier work this paper cites.
S. Kuksin, Growth and oscillations of solutions of nonlinear Schrödinger equation , Comm. Math. Phys. 178
1996
Earlier work this paper cites.
R. Moeckel, Transition tori in the five-body problem , J. Differential Equations 129
1996
Earlier work this paper cites.
J. Bourgain, On growth in time of Sobolev norms of smooth solutions of nonlinear Schrödinger equations in R D R^{D}
1997
Cited alongside, same era.
S. Kuksin, Oscillations in space-periodic nonlinear Schrödinger equations , Geom. Funct. Anal. 7
1997
Cited alongside, same era.
S. Kuksin, On turbulence in nonlinear Schrödinger equations , Geom. Funct. Anal. 7
1997
Cited alongside, same era.
A. Majda, D. McLaughlin, E. Tabak, A one-dimensional model for dispersive wave turbulence , J. Nonlinear Sci. 7
1997
Cited alongside, same era.
G. Staffilani, On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations
1997
Cited alongside, same era.
J. Bourgain, Refinements of Strichartz’s inequality and applications to 2D-NLS with critical nonlinearity , Intern. Mat. Res. Notices, 5
M. Berti, P. Bolle, A functional analysis approach to Arnold diffusion , Ann. Inst. H. Poincar? Anal. Non Lin?aire 19
2002
Later among the works it cites.
G. Contreras, G. Paternain, Connecting orbits between static classes for generic Lagrangian systems , Topology 41
2002
Later among the works it cites.
R. Moeckel, Generic drift on Cantor sets of annuli , Celestial mechanics (Evanston, IL, 1999), 163–171, Contemp. Math., 292
2002
Later among the works it cites.
T. Cazenave, Semilinear Schrödinger equations , Courant Lect. Notes in Math. 10
2003
Later among the works it cites.
A. Delshams, R. de la Llave, T. M. Seara, A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results , Electron. Res. Announc. Amer. Math. Soc. 9
2003
Later among the works it cites.
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1998
Cited alongside, same era.
J. Bourgain, Quasi-periodic solutions of Hamiltonian perturbations of 2 D 2D linear Schrödinger equations
1998
Cited alongside, same era.
S. Bolotin, D. Treschev, Unbounded growth of energy in nonautonomous Hamiltonian systems , Nonlinearity 12
1999
Cited alongside, same era.
J. Bourgain, Global solutions of nonlinear Schrödinger equations American Math. Society Colloquium Publications, 46
1999
Cited alongside, same era.
J. Bourgain, Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential
1999
Cited alongside, same era.
J. Bourgain, Nonlinear Schrödinger equations. Hyperbolic equations and frequency interactions (Park IAS/Park City Math. Ser., 5, Amer. Math. Soc., Providence, RI, 1999
1999
Cited alongside, same era.
J. Bourgain, On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
1999
Cited alongside, same era.
P. Kramer, J. Biello, Y. Lvov, Application of weak turbulence theory to FPU model , Proc. Int. Conf. Dyn. Syst. and Diff. Eq. (Wilmington, NC, 2002), Discrete Contin. Dyn. Syst. 2003, suppl., 482–491
2003
Later among the works it cites.
J. Bourgain, Remarks on stability and diffusion in high-dimensional Hamiltonian systems and partial differential equations
2004
Later among the works it cites.
C.-Q. Cheng, J. Yan, Existence of diffusion orbits in a priori unstable Hamiltonian systems J. Differential Geom. 67
2004
Later among the works it cites.
J. Mather, Arnold diffusion. I. Announcement of results , J. Math. Sci. (N. Y.) 124
2004
Later among the works it cites.
D. Treschev, Evolution of slow variables in a priori unstable Hamiltonian systems , Nonlinearity 17
2004
Later among the works it cites.
J. Bourgain, V. Kaloshin, On diffusion in high-dimensional Hamiltonian systems , J. Funct. Anal. 229
2005
Later among the works it cites.
Merle, F., Raphaël, P., Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation
2005
Later among the works it cites.
A. Delshams, R. de la Llave, T. M. Seara, A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model , Mem. Amer. Math. Soc. 179
2006
Later among the works it cites.
T. Tao, Nonlinear dispersive equations: Local and global analysis , CBMS Reg. Conf. Series in Math., 106
2006
Later among the works it cites.
J. Bourgain, W.-M. Wang, Diffusion bound for a nonlinear Schrödinger equation
2007
Later among the works it cites.
R. DeVille, P. Milewski, R. Pignol, E. Tabak, Esteban, E. Vanden-Eijnden, Nonequilibrium statistics of a reduced model for energy transfer in waves , Comm. Pure Appl. Math. 60
2007
Later among the works it cites.
F. Planchon, P. Raphaël, Existence and stability of the log-log blowup dynamics for the L 2 L^{2} -critical nonlinear Schrödinger equation in a domain
2007
Later among the works it cites.
W. Craig, editor, Hamiltonian dynamical systems and applications, Proceedings of the Advanced Study Institute on Hamiltonian Dynamical Systems and Applications , NATO Science for Peace and Security Series B: Springer - Verlag, (2008) XVI, 441 pp
2008
Closest in time.
V. Kaloshin, M. Levi, An example of Arnold diffusion for near integrable hamiltonians , Bull. AMS 45
2008
Closest in time.