简介：Wededuceacompletewavepropagationequationthatincludesinhomogeneityofthedielectricconstantandpresentthispropagationequationincompactvectorform.Althoughsimilarequationsareknowninnarrowfieldssuchasradiowavepropagationintheionosphereandelectromagneticandacousticwavepropagationinstratifiedmedia,wedevelophereanovelapproachofusingsuchequationsinthemodelingoflaserbeampropagationinnonlinearmedia.Ourapproachsatisfiesthecorrespondenceprinciplesinceinthelimitofzero-lengthwavelengthitreducesfromphysicaltogeometricaloptics.

简介：Inthispaper,wederivealawoflargenumbersunderthenonlinearexpectationgeneratedbybackwardstochasticdifferentialequationsdrivenbyG-Brownianmotion.

简介：ThispaperisconcernedwiththeexistenceandthenonlinearasymptoticstabilityoftravelingwavesolutionstotheCauchyproblemforasystemofdissipativeevolutionequations{ξt=-θx+βξxx,θt=vξx+(ξθ)x+αθxx,withinitialdataandendstates(ξ,θ)(x,0)=(ξ0,θ0)(x)→(ξ±,θ±)asx→±∞.Weobtaintheexistenceoftravelingwavesolutionsbyphaseplaneanalysisandshowtheasymptoticnonlinearstabilityoftravelingwavesolutionswithoutrestrictionsonthecoefficientsαandvbythemethodofenergyestimates.

简介：Inthispaper,weestablishanexistencecriterionoftriplepositivesolutionsofaclassofnonlinearfourth-orderthree-pointboundaryvalueproblembytheLeggettWilliamsfixedpointtheorem.Theinterestingpointisthatthenonlineartermisinvolvedwithalllow-levelderivatives.

简介：Inthispaper,weconsidertheuniformstabilityanduniformlyasymptoticalstabilityofnonlinearimpulsiveinfinitedelaydifferentialequations.InsteadofputtingallcomponentsofthestatevariablexinoneLyapunovfunction,severalLyapunov-Razumikhinfunctionsofpartialcomponentsofthestatevariablexareusedsothattheconditionsensuringthatstabilityaresimplerandlessrestrictive;moreover,examplesarediscussedtoillustratetheadvantageoftheresultsobtained.

简介：Nonlinearacousticpropagationgeneratedbyapistoninafinitehornisnumericallystudied.Aquasi-one-dimensionalnonlinearmodelwithvaryingcross-sectionuseshigh-orderlow-dispersionnumericalschemestosolvethegoverningequation.Becauseofthenonlinearwavedistortionandreflectedsoundwavesatthemouth,broadbandtime-domainimpedanceboundaryconditionsareemployed.Theimpedanceapproximationcanbeoptimizedtoidentifythecomplex-conjugatepole-residuepairsoftheimpedancefunctions,whichcanbecalculatedbyfastandefficientrecursiveconvolution.Thenumericalresultsagreeverywellwithexperimentaldatainthesituationsofweaknonlinearwavepropagationinanexponentialhorn,itisshownthatthemodelcandescribethebroadbandcharacteristicscausedbynonlineardistortion.Moreover,finite-amplitudeacousticpropagationintypesofhornsissimulated,includinghyperbolic,conical,exponentialandsinusoidalhorns.Itisfoundthatsoundpressurelevelsatthehornmoutharestronglyaffectedbythehornprofiles,thedrivingvelocityandfrequencyofthepiston.Thepaperalsodiscussestheinfluenceofthehorngeometryonnonlinearwaveformdistortion.

简介：Byusingtherefinementofthestandardintegralaveragingtechnique,weobtainsomeoscillationcriteriaforsecondordermixednonlinearellipticequations.Theresultsestablishedinthispaperextendandimprovesomeexistingoscillationcriteriaforhalf-linearPDEintheliterature.

简介：Theprimaryresonancesofaquadraticnonlinearsystemunderweakandstrongexternalexcitationsareinvestigatedwiththeemphasisonthecomparisonofdifferentanalyticalapproximateapproaches.Theforcedvibrationofsnap-throughmechanismistreatedasaquadraticnonlinearoscillator.TheLindstedt-Poincar′emethod,themultiple-scalemethod,theaveragingmethod,andtheharmonicbalancemethodareusedtodeterminetheamplitude-frequencyresponserelationshipsofthesteady-stateresponses.Itisdemonstratedthatthezeroth-orderharmoniccomponentsshouldbeaccountedintheapplicationoftheharmonicbalancemethod.Theanalyticalapproximationsarecomparedwiththenumericalintegrationsintermsofthefrequencyresponsecurvesandthephaseportraits.Supportedbythenumericalresults,theharmonicbalancemethodpredictsthatthequadraticnonlinearitybendsthefrequencyresponsecurvestotheleft.Iftheexcitationamplitudeisasecond-ordersmallquantityofthebookkeepingparameter,thesteady-stateresponsespredictedbythesecond-orderapproximationoftheLindstedtPoincar′emethodandthemultiple-scalemethodagreequalitativelywiththenumericalresults.Itisdemonstratedthatthequadraticnonlinearsystemimpliessofteningtypenonlinearityforanyquadraticnonlinearcoefficients.

简介：自相关函数并且有非线性的推迟时间的反馈的一个自治随机的系统跨关联被使用随机的模拟方法调查。在一个自治随机的系统的关联上二次的推迟时间的反馈和立方的推迟时间的反馈的角色之间有突出的差别。在二次的推迟时间的反馈下面，非线性的时间延期没能改进自治随机的系统的吵闹的状态，自相关单调地减少到零，并且跨关联的增加单调地到零与腐烂时间。在立方的推迟时间的反馈下面，非线性的时间延期能改进自治随机的系统的吵闹的状态；自相关和跨关联的表演期刊摆动和变细，最后与腐烂时间趋于到零。比较系统在之间的关联与非线性的推迟时间的反馈和线性推迟时间的反馈，我们发现非线性的推迟时间的反馈降低自治随机的系统的关联力量。

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简介：Inthispaper,weconsiderexistenceanduniquenessofpositivesolutionstothreecouplednonlinearSchrdingerequationswhichappearinnonlinearoptics.Weusethebehaviorsofminimizingsequencesforaboundtoobtaintheexistenceofpositivesolutionsforthreecoupledsystem.Toprovetheuniquenessofpositivesolutions,weusetheradialsymmetryofpositivesolutionstotransformthesystemintoanordinarydifferentialsystem,andthenintegratethesystem.Inparticular,forN=1,weprovetheuniquenessofpositivesolutionswhen0≤β=μ1=μ2=μ3orβ>max{μ1,μ2,μ3}.

简介：Inthispaper,theHyers-Ulamstabilityofathird-ordernonlineardifferentialequationisinvestigated.BytheintegratingmethodandaGronwalltypeinequality,thestabilityresultsareobtainedindifferentsituationsonaboundeddomain.Then,thestudyisextendedtonth-ordernonlineardifferentialequations.

简介：Usingastrongnonlinearsaturationabsorptioneffectisonetechniqueforbreakingthroughthediffractionlimit.Inthistechnique,formationofadynamicandreversibleopticalpinholechannelandtransientsuperresolutioniscritical.Inthiswork,apump–probetransientdetectionandobservation–experimentalsetupisconstructedtoexploretheformationprocessdirectly.AGe2Sb2Te5thinfilmwithstrongnonlinearsaturationabsorptionisinvestigated.Thedynamicevolutionoftheopticalpinholechannelisdetectedandimaged,andthetransientsuperresolutionspotisdirectlycapturedexperimentally.Resultsverifythatthesuperresolutioneffectoriginatesfromthegenerationofanopticalpinholechannelandthattheformationoftheopticalpinholechannelisdynamicandreversible.Agoodmethodisprovidedfordirectdetectionandobservationofthetransientprocessofthesuperresolutioneffectofnonlinearthinfilms.

简介：Inthispaper,weinvestigatestochasticasymptoticstabilityofthezerosolutionforcertainthird-ordernonlinearstochasticdelaydifferentialequationsbyconstructingLyapunovfunctionals.

简介：Inthispaper,theClarkson–Kruskaldirectapproachisemployedtoinvestigatetheexactsolutionsofthe2-dimensionalrotationalEulerequationsfortheincompressiblefluid.Theapplicationofthemethodleadstoasystemofcompletelysolvableordinarydifferentialequations.Severalspecialcasesarediscussedandnovelnonlinearexactsolutionswithrespecttovariablesxandyareobtained.Itisofinteresttonoticethatthepressurepisobtainedbythesecondkindofcurvilinearintegralandthecoefficientsofthenonlinearsolutionsaresolitarywavetypefunctionsliketanh(kt/2)andsech(kt/2)duetotherotationalparameterk=0.SuchphenomenonneverappearintheclassicalEulerequationswhereintheCoriolisforcearisingfromthegravityandEarth’srotationisignored.Finally,illustrativenumericalfiguresareattachedtoshowthebehaviorsthattheexactsolutionsmayexhibit.

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简介：Bythemethodofdynamicalsystem,weconstructtheexacttravellingwavesolutionsofanewHamiltonianamplitudeequationandtheOstrovskyequation.Basedonthismethod,thenewexacttravellingwavesolutionsofthenewHamiltonianamplitudeequationandtheOstrovskyequation,suchassolitarywavesolutions,kinkandanti-kinkwavesolutionsandperiodictravellingwavesolutions,areobtained,respectively.

简介：All-opticalcanonicallogicunitsat40Gb/susingbidirectionalfour-wavemixing(FWM)inhighlynonlinearfiberareproposedandexperimentallydemonstrated.Cleartemporalwaveformsandcorrectpatternstreamsaresuccessfullyobservedintheexperiment.Thisschemecanreducetheamountofnonlineardevicesandenlargethecomputingcapacitycomparedwithgeneralones.ThenumericalsimulationsaremadetoanalyzetherelationshipbetweentheFWMefficiencyandthepositionoftwointeractionalsignals.

简介：TheexistenceandorbitalinstabilityofstandingwavesforthegeneralizedthreedimensionalnonlocalnonlinearSchr¨odingerequationsisstudied.Bydefiningsomesuitablefunctionalsandaconstrainedvariationalproblem,wefirstestablishtheexistenceofstandingwaves,whichrelysontheinnerstructureoftheequationsunderconsiderationtoovercomethedrawbackthatnonlocaltermsviolatethespace-scaleinvariance.Wethenshowtheorbitalinstabilityofstandingwaves.Theargumentsdependupontheconservationlawsofthemassandoftheenergy.