简介：WediscussseparabilityofsolutionstoaSchr?dingerequationthatdescribesacompositequantumsystemandgivesomekindsofHamiltoniansH(t)suchthatthesolutiontoSchr?dingerequationinducedbyH(t)isseparableatanytimeprovidedthatitisseparableatt=0.Forexample,weprovethatiftheHamiltonianHistime-independentandequalstotheproductPA■PBoftwoprojectionsonthesubsystemsKAandKB,respectively,thenthestate|ψ(t)ofthecompositesystemstartingfromaseparableinitial|ψ(0)=|ψA■|ψBisseparableforallt∈[0,T]ifandonlyifeither|ψAisaneigenstateofPA,or|ψBisaneigenstateofPB.

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

简介：Thispaperconsiderstheone-dimensionaldissipativecubicnonlinearSchrdingerequationwithzeroDirichletboundaryconditionsonaboundeddomain.Theequationisdiscretizedintimebyalinearimplicitthree-levelcentraldifferencescheme,whichhasanalogousdiscreteconservationlawsofchargeandenergy.Theconvergencewithtwoordersandthestabilityoftheschemeareanalysedusingaprioriestimates.Numericaltestsshowthatthethree-levelschemeismoreefficient.

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：WeinvestigatethePainlevéintegrabilityofnonautonomousnonlinearSchrdinger(NLS)equationswithbothspace-andtime-dependentdispersion,nonlinearity,andexternalpotentials.ThePainlevéanalysisiscarriedoutwithoutusingtheKruskal'ssimplification,whichresultsinmoregeneralizedformofinhomogeneousequations.TheobtainedequationsareshowntobereducibletothestandardNLSequationbyusingapointtransformation.WealsoconstructthecorrespondingLaxpairandcarryoutitsKundu-typereductiontothestandardLaxpair.SpecialcasesofequationsfromchoosinglimitedformofcoefficientscoincidewiththeequationsfromthepreviousPainlevéanalysesand/orbecomeunknownnewequations.

简介：Basedonthecovariantprolongationstructuretechnique,weconstructtheintegrablehigher-orderdeformationsofthe(2+1)-dimensionalHeisenbergferromagnetmodelandobtaintheirsu(2)×R(λ)prolongationstructures.ByassociatingthesedeformedmultidimensionalHeisenbergferromagnetmodelswiththemovingspacecurveinEuclideanspaceandusingtheHasimotofunction,wederivetheirgeometricalequivalentcounterparts,i.e.,higher-order(2+1)-dimensionalnonlinearSchrdingerequations.

简介：采用算子分裂方法将辐射流体力学方程组分裂为对流项和刚性源项,并设计了一种高效求解刚性源项方程组的数值方法.数值实验表明:该方法对时间步长不敏感,计算精度能够满足工程计算要求.在不对方程组做任意近似的情况下,数值给出了较长时间内火球物理参量的空间分布.该结果与实际强爆炸中的一些经验公式吻合较好.