 -critical case 10
 -concentration 37
-critical case 9
-cutoff 124
( = scaling exponent) 6
Admissible 13
Almost periodic solutions 143
Ball multiplier 35
Bloch waves 155
Blowup solutions 17
Brascamp — Lieb inequality 136
Canonical coordinates 5
Compactness property 44
Conformal NLS 17
Critical 6
Decay estimate 11
Defocusing 5
Derivative nonlinear Schroedinger equations 14
Dirichlet 144
Energy estimates 50
Exponential pair 13
Exponential sum 108
Fermi-golden rule 27
Focusing 5
Gauge transformation 15
Gibbs measure 106
Gibbs measures 4
Glassey's viriel inequality 8
Global scattering in the energy space 11
Global scattering with decay 10
Groundstate 8
Hamiltonian 106
Hamiltonian perturbation 143
Hamiltonian vector field 93
Hartree 133
Hausdorff — Young inequality 116
Hermith polynomial 130
Initial value problem (IVP) 1
Integral equation 10
interactions 153
Invariant Gibbs measures 122
Invariant tori 143
Kakeya set 33
KAM (Kolmogorov — Arnold — Moser) 4
KdV-equation 79
Lattice points 146
Linear scattering 19
| Linear Schroedinger equations 29
Linear Schroedinger group 33
m-admissible 93
Maximal existence time 7
Maximal inequalities 12
Melnikov's theorem 152
Morawetz' inequality 11
Nonlinear coupling 173
Nonlinear Schroedinger equation (NLS for short) 1
Nonlinear string equation 93
Nonsqueezing theory 83
Normal frequencies 144
Oscillatory integral 108
Periodic boundary conditions 105 144
Periodic solutions 143
Periodic Strichartz inequalities 108
Pseudo-conformal conservation law 6
Quasi-periodic solutions 143
Random fields 129
Resonance relation 149
Restriction conjecture 12 33
Restriction norm 109
Scattering 10
Secular modes 20
Short range 153
Small data scattering 10
Smoothing inequalities 12
Space-time norms 109
Strichartz' inequality 11
Sturm — Liouville operator 143
Subcritical 6
Symplectic capacities 93
Symplectic capacity 83
Symplectic Hilbert space 5 80
Symplectic structure 93
Symplectic transformations 148
Tangential frequencies 144
The nonlinear wave equation (NLW) 2
Tomas — Stein restriction theorem 12
Truncated Gibbs measures 175
Wave equation 10
Weighted Wiener measure 123
Wick-ordering 130
Wiener measure 106
Young's inequality 40
Zakharov system 4
Zakharov systems 173
“Separated-cluster” structure 156
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