简介：Weexperimentallyinvestigatedthenonlinearopticalresponseinfew-layeroxidizedblackphosphorus(OBP)bythefemtosecondZ-scanmeasurementtechnique,andfoundthatOBPnotonlypossessesstrongultrafastsaturableabsorptionbutalsoanonlinearself-defocusingeffectthatisabsentinblackphosphorus(BP).Thesaturableabsorptionpropertyoriginatesmainlyfromthedirectbandstructure,whichisstillmaintainedinOBP.Theemergenceofself-defocusingmightoriginatefromthecombinedconsequencesoftheoxygen-induceddefectsinBP.Ourexperimentalfindingsmightconstitutethefirstexperimentalevidenceonhowtodynamicallytuneitsnonlinearproperty,offeringaninroadintailoringitsopticalpropertiesthroughchemicalmodification(oxidation,introducingdefects,etc.).Theversatileultrafastnonlinearopticalproperties(saturableabsorptionandself-defocusing)implyasignificantpotentialofthelayeredOBPinthedevelopmentofunprecedentedoptoelectronicdevices,suchasmodelockers,opticalswitches,laserbeamshapers,andwavelengthconverters.

简介：Inordertoprovidethebasisforparameterselectionofvocaldiseasesclassification,anonlineardynamicmodelingmethodisproposed.Abiomechanicalmodelofvocalcordswithpolyporparalysis,whichcouplestoglottalairflowtoproducelaryngealsoundsource,isintroduced.Andthenthefundamentalfrequencyanditsperturbationparametersaresolved.Poincaresectionandbifurcationdiagramareappliedtononlinearanalysisofmodelvibration.Bychangingthepathologicalparametersorsubglottalpressure,thechangesoffundamentalfrequencyandLyapunovexponentsareanalyzed.Thesimulationresultsshowthat,vocalcordparalysisreducesthefundamentalfrequency,andthechaosoccursonlywithinacertainpressurerange;whilevocalcordwithapolypdon’treducethefundamentalfrequency,chaosdistributesthroughouttheentirerangeofpressure.Thereforethisstudyishelpfulforclassificationofpolypandparalysisbytheacousticdiagnoses.

简介：Oneofthemostinterestingproblemsofnonlineardifferentialequationsistheconstructionofpartialsolutions.Anewmethodispresentedinthispapertoseekspecialsolutionsofnonlineardiffusionequations.ThismethodisbasedonseekingsuitablefunctiontosatisfyBernolliequation.Manynewspecialsolutionsareobtained.

简介：Weinvestigatethenonlinearresponseofterahertz(THz)metamaterialperfectabsorbersconsistingofelectricsplitringresonatorsonGaAsintegratedwithapolyimidespacerandgoldgroundplane.Theseperfectabsorbersonbulksemi-insulatingGaAsarecharacterizedusinghigh-fieldTHztime-domainspectroscopy.Theresonancefrequencyredshifts20GHzandtheabsorbanceisreducedby30%astheincidentpeakfieldisincreasedfrom30to300kV/cm.ThenonlinearresponsearisesfromTHzfielddriveninterbandtransitionsandintervalleyscatteringintheGaAs.ToeliminatetheFresnellossesfromtheGaAssubstrate,wedesignandfabricateaflexiblemetamaterialsaturableperfectabsorber.Theabilitytocreatenonlinearabsorbersenablesappealingapplicationssuchasopticallimitingandself-focusing.

简介：WestudytheDirichletproblemassociatedtostronglynonlinearparabolicequationsinvolvingp(x)structureinW_0~(1,x)L~(p(x))(Q).WeprovetheexistenceofweaksolutionsbyapplyingGalerkin'sapproximationmethod.

简介：ThisstudyconcernscalculationofphasedarraybeamfieldsofthenonlinearRayleighsurfacewavesbasedontheintegralsolutionsforanonparaxialwaveequation.SincetheparabolicapproximationmodelfordescribingthenonlinearRayleighwaveshascertainlimitationsinmodelingthesoundbeamfieldsofphasedarrays,amoregeneralmodelequationandintegralformsofquasilinearsolutionsareintroduced.SomefeaturesofsteeredandfocusedbeamGeldsradiatedfromalinearphasedarrayofthesecondharmonicRayleighwavearepresented.

简介：Inthispaper,byusingtheGuo-Krasnoselskii'sfixed-pointtheorem,weestablishtheexistenceandmultiplicityofpositivesolutionsforafourth-ordernonlineareigenvalueproblem.Thecorrespondingexamplesarealsoincludedtodemonstratetheresultsweobtained.

简介：Westudythedynamicsofthecubic–quinticnonlinearSchr?dingerequationbythesymplecticmethod.Thebehaviorsoftheequationarediscussedwithharmonicallymodulatedinitialconditions,andthecontributionsfromthequintictermarediscussed.Weobservetheellipticorbit,homoclinicorbitcrossing,quasirecurrence,andstochasticmotionwithdifferentnonlinearparametersinthissystem.Numericalsimulationsshowthatthechangingprocessesofthemotionofthesystemandthetrajectoriesinthephasespacearevariousfordifferentcubicnonlinearparameterswiththeincreaseofthequinticnonlinearparameter.

简介：BasedonthecontinuityofthederivativesoftheNon-UniformRationalB-Splines(NURBS)curveandtheJaumannstrainmeasure,thepresentpaperadoptedthepositioncoordinatesofthecontrolpointsasthedegreesoffreedomanddevelopedaplanarrotation-freeEuler-Bernoullibeamelementforisogeometricanalysis,wherethederivativesofthefieldvariableswithrespecttothearc-lengthwereexpressedasthesumoftheweightedsumofthepositioncoordinatesofthecontrolpoints,andtheNURBSbasisfunctionswereusedastheweightfunctions.Furthermore,theconceptofbendingstripwasusedtoinvolvetherigidconnectionbetweenmultiplepatches.Severaltypicalexampleswithgeometricnonlinearitieswereusedtodemonstratetheaccuracyandeffectivenessoftheproposedalgorithm.Thepresentedformulationfullyaccountsforthegeometricnonlinearitiesandcanbeusedtostudythesnap-throughandsnap-backphenomenaofflexiblebeams.

简介：Inthispaper,severalnewconstant-amplitudeandvariable-amplitudewavesolutions(namely,travelingwavesolutions)ofageneralizednonlinearSchrdingerequationareinvestigatedbyusingtheextendedhomogeneousbalancemethod,wherethebalancemethodisappliedtosolvetheRiccatiequationandthereducednonlinearordinarydifferentialequation,respectively.Inaddition,stabilityanalysisofthosesolutionsarealsoconductedbyregularphaseplanetechnique.

简介：

简介：Thequasilinearhyperbolicequationwithnonlineardampingisconsideredinthispaper,anewasymptoticprofileforthesolutiontotheequationisobtainedbysuitablychoosingtheinitialdataofthecorrespondingparabolicequation,theconvergenceratesofthenewprofilearebetterthanthatobtainedbyNishihara(1997,J.DifferentialEquations137,384-395)andH.-J.Zhao(2000,J.DifferentialEquations167,467-494).

简介：WestudythegeneralizedDarbouxtransformationtothethree-componentcouplednonlinearSchr¨odingerequation.First-andsecond-orderlocalizedwavesareobtainedbythistechnique.Infirst-orderlocalizedwave,wegettheinteractionalsolutionsbetweenfirst-orderroguewaveandone-dark,one-brightsolitonrespectively.Meanwhile,theinteractionalsolutionsbetweenone-breatherandfirst-orderroguewavearealsogiven.Insecond-orderlocalizedwave,one-dark-one-brightsolitontogetherwithsecond-orderroguewaveispresentedinthefirstcomponent,andtwo-brightsolitontogetherwithsecond-orderroguewavearegainedrespectivelyintheothertwocomponents.Besides,weobservesecond-orderroguewavetogetherwithone-breatherinthreecomponents.Moreover,byincreasingtheabsolutevaluesoftwofreeparameters,thenonlinearwavesmergewitheachotherdistinctly.Theseresultsfurtherrevealtheinterestingdynamicstructuresoflocalizedwavesinthethree-componentcoupledsystem.

简介：Inthispaper,weconsideranonlinearsystemofreactiondiffusionequationsarisingfrommathematicalneuroscienceandtwononlinearscalarreactiondiffusionequationsundersomeassumptionsontheircoefficients.Themainpurposeistocoupletogetherlinearizedstabilitycriterion(theequivalenceofthenonlinearstability,thelinearstabilityandthespectralstabilityofthestandingpulsesolutions)andEvansfunctionstoaccomplishtheexistenceandinstabilityofstandingpulsesolutionsofthenonlinearsystemofreactiondiffusionequationsandthenonlinearscalarreactiondiffusionequations.TheEvansfunctionsforthestandingpulsesolutionsareconstructedexplicitly.

简介：在这份报纸，一条直接概率的途径(DPA)被介绍为能是任何一个的环境负担激动的非线性的系统提出并且解决时刻方程一静止或nonstationary随机过程。建议方法有的优点从起始的条件和相应外部刺激的统计特征直接获得回答时刻。首先，回答时刻方程直接基于DPA被导出，它完全独立于它?后来，关于关联的特定的假设都不刺激组织的/filtering途径被做。由在Gaussian闭合下面解决他们，回答时刻能被获得。随后，为时刻方程的数字答案的一个多尺度的算法被利用改进计算效率并且避免许多墙钟时间。最后，有蒙特卡罗(MC)模拟的结果的比较给好同意。而且，多尺度的算法的优点被一个设计例子也以效率表明。

简介：Inthispaper,westudythenonexistenceandlongtimebehaviorofweaksolutionforthedegenerateparabolicequation?_tu~n=u~mdiv(|▽_u~m|~(p-2)▽u~m)+γ|▽u~m|~p+βu~nwithzeroboundarycondition.Blow-uptimeisderivedwhentheblow-updoesoccur.

简介：这份报纸与uncertain-but-bounded参数或起始的条件为非线性的系统的动态反应分析用衍生物信息建议一个新非恼人的混合间隔方法。这个方法与存在多项式近似间隔方法相比提供更紧密的答案范围。用Chebyshev基础的间隔算术和用一般形式的间隔算术修改了仿射的基础因为多项式被开发为间隔计算获得更紧密的界限。为了进一步减少overestimation，由间隔算术的包的效果引起了，当动态回答是关于所有不明确的变量的monotonic时，动态回答的衍生物信息被用来完成准确溶液。最后，有非线性的二个典型数字例子被使用特别地，表明建议混合间隔方法的有效性它有效地为特定的timepoints控制overestimation的能力。

简介：Inthispaper,aclassofparameter-freefilledfunctionsisproposedforsolvingbox-constrainedsystemofnonlinearequations.Firstly,theoriginalproblemisconvertedintoanequivalentglobaloptimizationproblem.Subsequently,aclassofparameter-freefilledfunctionsisproposedforsolvingtheproblem.Somepropertiesofthenewclassoffilledfunctionsarestudiedanddiscussed.Finally,analgorithmwhichneithercomputesnorexplicitlyapproximatesgradientsduringminimizingthefilledfunctionsispresented.Theglobalconvergenceofthealgorithmisalsoestablished.Theimplementationofthealgorithmonseveraltestproblemsisreportedwithsatisfactorynumericalresults.

简介：Byusingthemethodofdynamicalsystem,theexacttravellingwavesolutionsofthecouplednonlinearSchrdinger-KdVequationsarestudied.Basedonthismethod,allphaseportraitsofthesystemintheparametricspacearegiven.Allpossibleboundedtravellingwavesolutionssuchassolitarywavesolutionsandperiodictravellingwavesolutionsareobtained.WiththeaidofMaplesoftware,thenumericalsimulationsareconductedforsolitarywavesolutionsandperiodictravellingwavesolutionstothecouplednonlinearSchrdinger-KdVequations.Theresultsshowthatthepresentedfindingsimprovetherelatedpreviousconclusions.

简介：Inthispaper,themodifiedextendedtanhmethodisusedtoconstructmoregeneralexactsolutionsofa(2+1)-dimensionalnonlinearSchr¨odingerequation.WiththeaidofMapleandMatlabsoftware,weobtainexactexplicitkinkwavesolutions,peakonwavesolutions,periodicwavesolutionsandtheir3Dimages.