Schrödinger and wave equations
DISPERSION FOR THE WAVE AND SCHRÖDINGER EQUATIONS OUTSIDE A BALL AND COUNTEREXAMPLES
... Melrose and Taylor parametrix was used in [ 28 ] to prove that Strichartz estimates for the wave equation do hold as in R d (except for the ...either wave or Schr¨ odinger ...
45
The Cauchy Problem for Schrödinger-Debye equations
... the wave is described by the parameter n 2 ...c and k is the wave vector of the incident electromagnetic ...dimensionless equations keeping however a parameter τ which for applications has to ...
10
Rational normal forms and stability of small solutions to nonlinear Schrödinger equations
... nonlinear wave equation– and the stability result were obtained for almost every value of these ...nonlinear Schrödinger equation on the two dimensional torus it is proved in [CKSTT10] that the high ...
54
On the Wave Turbulence Theory for the Nonlinear Schrödinger Equation with Random Potentials
... type equations and more, there is no compelling analytic or even phenomenological ...mathematics and chaos ...equation and the other one needed to approximate the behavior of the kinetic ...
13
STABILITY OF STEADY STATES FOR HARTREE AND SCHRÖDINGER EQUATIONS FOR INFINITELY MANY PARTICLES
... Solutions of (5) with an infinite number of particles were studied previously in [5, 6, 7, 31] for exemple, and more recently in [8, 9, 24, 25]. The derivation of equation (5) from many body quantum mechanics has ...
47
Stabilisation of wave equations on the torus with rough dampings
... framework and Sjöstrand-Zworski [ 49 ] in the semi-classical setting) and in the framework of defect measures by Fermanian–Kammerer [ 20 ], Miller [ 37 , 38 , 39 ], Nier [ 41 ], Fermanian–Kammerer-Gérard [ ...
30
Stability of periodic waves of 1D cubic nonlinear Schrödinger equations
... NONLINEAR SCHRÖDINGER EQUATIONS STEPHEN GUSTAFSON, STEFAN LE COZ, AND TAI-PENG TSAI ...dnoidal and snoidal elliptic functions as spatially-periodic standing wave solutions of the 1D ...
43
Periodic modulations controlling Kuznetsov-Ma soliton formation in nonlinear Schrödinger equations
... arise, and consequently gained increasing interest, in various phys- ical systems [ 1 ...] and the atmosphere [ 7 ...average wave height, appear from nowhere and disappear without a trace [ 8 ...
9
On critical and supercritical blow-up for the semilinear heat and wave equations
... solutions linéaires. Récemment cette étude des résonances a permis par exemple une meilleure com- préhension de la turbulence et de la répartition de l’énergie entre les différentes échelles spatiales pour l’équation de ...
506
Exponential integrators for nonlinear Schrödinger equations with white noise dispersion
... stochastic Schrödinger equation ...used and studied, as witnessed by the recent review ...(nonlinear) Schrödinger equation can be found in, for example, [20, 5, 4, 9, 16, 10, 7, 8, 6] and ...
17
Well-posedness and smoothing effect for generalized nonlinear Schrödinger equations: the quadratic interaction case
... L and established the local existence and the smoothing effect of the solutions assuming that F is a polynomial and s ≥ s 0 , the index s 0 being sufficiently ...
47
Comments on ``The Depth-Dependent Current and Wave Interaction Equations: A Revision''
... The wave-averaged conservation of momentum can take essentially two forms, one for the mean flow momentum only, and the alternative form for the full momentum, which includes the wave pseudo-momentum ...
6
Null Controllability for Wave Equations with Memory
... R´esum´e Nous ´etudions le contrˆole vers l’´equilibre de l’´equations des ondes avec m´emoire. Ceci ´exige non seulement de contrˆoler le d´eplacement et la vitesse de l’onde consid´er´ee, mais aussi d’assurer ...
25
LONG TIME SOLUTIONS FOR QUASI-LINEAR HAMILTONIAN PERTURBATIONS OF SCHRÖDINGER AND KLEIN-GORDON EQUATIONS ON TORI
... for almost any value of the mass m in the interval [1, 2] and where β is any real number in the open in- terval (3, 4). The second factor in the r.h.s. of the above inequality represents a loss of derivatives ...
50
Maximum Decay Rate for Finite-Energy Solutions of Nonlinear Schrödinger Equations
... [6] T. Cazenave. An introduction to nonlinear Schr¨ odinger equations, volume 26 of Textos de M´etodos Matem´ aticos. Instituto de Matem´ atica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, third ...
13
Resonant averaging for small-amplitude solutions of stochastic nonlinear Schrödinger equations
... Resonant averaging for small-amplitude solutions of stochastic nonlinear Schr¨ odinger equations Sergei Kuksin CNRS and IMJ, Universit´e Paris Diderot-Paris 7, Paris, France kuksin@math.[r] ...
40
On the dynamics of energy-critical focusing wave equations
... Mots clés : équation des ondes, non linéarité énergie-critique, explosion, multi-soliton Résumé : Cette thèse est consacrée à l'étude du comportement global des solutions de l'équation des ondes énergie-critique ...
189
Constructive exact controls for semi-linear wave equations
... We consider a two-dimensional case for which Ω = (0, 1) 2 . The controllability time is equal to T = 3 and the control domain ω is depicted on Figure 1. Moreover, for any real constant c g , we consider the ...
33
Asymptotic analysis of numerical wave propagation in finite difference equations
... discussed the use of group velocity in analysing finite difference equations but does not derive a general equation for the amplitude or calculate the quantitative [r] ...
143
Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations
... linear and nonlinear subproblems are given by a spec- tral decomposition into Fourier basis functions, realized numerically by Fast Fourier techniques, and pointwise ...reduction and the fact that a ...
24