We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

Modified scattering for the Gross-Pitaevskii equation

00:00
subtitles
off
playback rate
1
subtitles
off
Englisch (auto-generated)
playback rate
0.25
0.5
0.75
1
1.25
1.5
1.75
2
quality
576p
 Cite
 Share
 Download Purchase
Institut des Hautes Études Scientifiques (IHÉS)
 Thomann, Laurent

Formal Metadata

Title
Modified scattering for the Gross-Pitaevskii equation
Title of Series
Part Number
4
Number of Parts
Author
License
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
We consider the cubic nonlinear Schrödinger equation with harmonic trapping. In the case when all but one directions are trapped, we prove modified scattering and construct modified wave operators for small initial and final data respectively. Actually, we prove that the asymptotic behavior of the solutions is given by a simpler equation, depending on the resonances of the GP equation, and we exhibit some particular solutions of it.
00:00
Mathematical singularitySpecial unitary groupDiscrete element methodSigma-algebraKnotMassUniform boundedness principleGradientNewton's law of universal gravitationFlow separationMoment (mathematics)Descriptive statisticsEigenvalues and eigenvectorsNichtlineares GleichungssystemConvolutionWaveTerm (mathematics)Product (business)Fourier seriesAlgebraic structureInitial value problemLinear mapNormal-form gameFamilyResonatorCondition numberParameter (computer programming)CoefficientSquare numberContinuum hypothesisResultantLink (knot theory)Integration by partsPhysical systemVariable (mathematics)SummierbarkeitMultilaterationPotenz <Mathematik>Normal (geometry)Functional (mathematics)MereologyMultiplication signHelmholtz decompositionOrder (biology)Dynamical systemProfil (magazine)Social classMortality rateManifoldINTEGRALCondensationScatteringDifferent (Kate Ryan album)Perturbation theoryLimit (category theory)Dimensional analysisVector potentialEstimatorObservational study2 (number)Color confinementMathematicsFrequencyModel theoryLaplace-OperatorFree groupEvoluteLinear subspaceCohen's kappaWell-formed formulaCubic graphState of matterDivisorLimit of a functionTorusPolynomialScaling (geometry)Derivation (linguistics)Phase transitionProof theoryGamma functionExistenceOrbitSpacetimeLocal ringCorrespondence (mathematics)TheoremStatistical hypothesis testingGoodness of fitDispersionsrelationDuality (mathematics)Thermodynamisches SystemRight angleDependent and independent variablesInsertion lossLengthPower (physics)Network topologyHamiltonian (quantum mechanics)Vector graphicsAbsolute valueSolid geometryMany-sorted logicIncidence algebraFood energyOperator (mathematics)ForestLine (geometry)Wave packetPoint (geometry)Projective planeString theoryPosition operatorInfinity1 (number)PerimeterStaff (military)Rule of inferenceStudent's t-testPopulation densitySeries (mathematics)Theory of relativityTotal S.A.ModulformGrothendieck topologyEnergy levelLattice (order)Maß <Mathematik>Decision theoryCoefficient of determinationBeat (acoustics)Directed graphCommutatorSpherical capLogicIntegerSet theoryQueue (abstract data type)Presentation of a groupMusical ensembleNumerical analysisConfiguration spaceStructural loadArchaeological field surveyThermal radiationPhysical lawFactory (trading post)Forcing (mathematics)Real numberComputer animationLecture/Conference
Transcript: Englisch(auto-generated)