简介:纸探讨率方程的明确的表达,经由客观时间衍生物,在连续统物理以内。客观性的概念被考察,区别与其意思相对Galilee的框架被限制为平衡方程的不变性的材料框架不在乎被做。客观时间衍生物被定义离开在欧几里德几何学的框架的集合以内不变的适当的地的张肌特性。率方程被要求包含客观时间衍生物并且与热力学的第二条法律一致。这里,客观时间衍生物的一般结构被建立,物理文学的已知的衍生物被显示是特别盒子。到改正想法,下次,一个率方程与高顺序的坡度经由Maxwell-Cattaneo方程的归纳为热传导的模型被考虑作为在Guyer-Krumhansl方程。热力学的限制被调查,热流动的选择衍生物,期望的效果在压力张肌上被导出。
简介:Basedonthetheoryofcalculusofvariation,somesuffcientconditionsaregivenforsomeEuler-LagrangcequationstobeequivalentlyrepresentedbyfiniteoreveninfinitemanyHamiltoniancanonicalequations.Meanwhile,somefurtherapplicationsforequationssuchastheKdVequation,MKdVequation,thegenerallinearEulerLagrangeequationandthecylindricshellequationsaregiven.
简介:Inthispaper,theclassicalLiegroupapproachisextendedtofindsomeLiepointsymmetriesofdifferentialdifferenceequations.ItrevealsthattheobtainedLiepointsymmetriescanconstituteaKac-Moody-Virasoroalgebra.
简介:Ellipticequationistakenasanansatzandappliedtosolvenonlinearwaveequationsdirectly.Morekindsofsolutionsaredirectlyobtained,suchasrationalsolutions,solitarywavesolutions,periodicwavesolutionsandsoon.Itisshownthatthismethodismorepowerfulingivingmorekindsofsolutions,soitcanbetakenasageneralizedmethod.
简介:这份报纸为numberresolved主人方程的推导论述波浪功能途径的全面评论,在mesoscopic系统为对运输和测量的描述使用。评论包含重要修正案,澄清在主人方程和他们的有效性的推导的微妙的点。这在这个题目上完成更早的工作。推导不假定弱结合,这被表明环境和水库,而是需要仅仅高偏导状况。这个条件为Markovian主人方程的有效性是很必要的,广泛地为对不同物理过程的现象学的描述使用。
简介:Weinvestigateanewclassofperiodicsolutionsto(2+1)-dimensionalKdVequations,byboththelinearsuperpositionapproachandthemappingdeformationmethod.Thesenewperiodicsolutionsaresuitablecombinationsoftheperiodicsolutionstothe(2+1)-dimensionalKdVequationsobtainedbymeansoftheJacobianellipticfunctionmethod,buttheypossessdifferentperiodsandvelocities.
简介:WepresentanF-expansionmethodforfindingperiodicwavesolutionsofnonlinearevolutionequationsinmathematicalphysics,whichcanbethoughtofasaconcentrationofextendedJacobiellipticfunctionexpansionmethodproposedrecently.ByusingtheF-expansion,withoutcalculatingJacobiellipticfunctions,weobtainsimultaneouslymanyperiodicwavesolutionsexpressedbyvariousJacobiellipticfunctionsforthevariantBoussinesqequations.Whenthemodulusmapproaches1and0,thehyperbolicfunctionsolutions(includingthesolitarywavesolutions)andtrigonometricsolutionsarealsogivenrespectively.
简介:Inthispaper,anextendedmethodisproposedforconstructingnewformsofexacttravellingwavesolutionstononlinearpartialdifferentialequationsbymakingamoregeneraltransformation.Forillustration,weapplythemethodtotheasymmetricNizhnik-Novikov-VesselovequationandthecoupledDrinfel'd-Sokolov-WilsonequationandsuccessfullycoverthepreviouslyknowntravellingwavesolutionsfoundbyChen'smethod[Y.Chen,etal.Chaos,SolitonsandFractals22(2004)675;Y.Chen,etal.Int.J.Mod.Phys.C4(2004)595].
简介:InthepresentpapertheLiesymmetricalnon-NoetherconservedquantityofthePoincaré-ChetaevequationsunderthegeneralinfinitesimaltransformationsofLiegroupsisdiscussed.First,weestablishthedeterminingequationsofLiesymmetryoftheequations.Second,theLiesymmetricalnon-Noetherconservedquantityoftheequationsisdeduced.
简介:ALaplacedecompositionalgorithmisadoptedtoinvestigatenumericalsolutionsofaclassofnonlinearpartialdiferentialequationswithnonlineartermofanyorder,utt+auxx+bu+cup+du2p1=0,whichcontainssomeimportantequationsofmathematicalphysics.Threedistinctinitialconditionsareconstructedandgeneralizednumericalsolutionsaretherebyobtained,includingnumericalhyperbolicfunctionsolutionsanddoublyperiodicones.Illustrativefiguresandcomparisonsbetweenthenumericalandexactsolutionswithdiferentvaluesofpareusedtotesttheefciencyoftheproposedmethod,whichshowsgoodresultsareachieved.
简介:Inthispaper,theClarkson–Kruskaldirectapproachisemployedtoinvestigatetheexactsolutionsofthe2-dimensionalrotationalEulerequationsfortheincompressiblefluid.Theapplicationofthemethodleadstoasystemofcompletelysolvableordinarydifferentialequations.Severalspecialcasesarediscussedandnovelnonlinearexactsolutionswithrespecttovariablesxandyareobtained.Itisofinteresttonoticethatthepressurepisobtainedbythesecondkindofcurvilinearintegralandthecoefficientsofthenonlinearsolutionsaresolitarywavetypefunctionsliketanh(kt/2)andsech(kt/2)duetotherotationalparameterk=0.SuchphenomenonneverappearintheclassicalEulerequationswhereintheCoriolisforcearisingfromthegravityandEarth’srotationisignored.Finally,illustrativenumericalfiguresareattachedtoshowthebehaviorsthattheexactsolutionsmayexhibit.
简介:Runge-Kuttamethodiswidelyappliedtosolvetheinitialvalueproblemofordinarydifferentialequations.TheimplicitRunge-Kuttawithbetternumericalstabilityforthenumericalintegrationofstiffdifferentialsystems,buttheformulatehastraditionallybeenonsolvingthenonlinearequationsresultingfromamodifiedNewtoniterationineverytime.Semi-implicitformulatehavethemajorcomputationallyadvantagethatitisnecessarytosolveonlylinearsystemsofalgebraicequationstofindtheKa.