简介：Inthispaper,aBoussinesqhierarchyinthebilinearformisproposed.ABacklundtransformationforthishierarchyispresentedandthenonlinearsuperpositionformulaisprovedrigorously.

简介：Byusingthemodifiedmappingmethod,wefindsomenewexactsolutionsofthegeneralizedBoussinesqequationandtheBoussinesq-Burgersequation.ThesolutionsobtainedinthispaperincludeJacobianellipticfunctionsolutions,combinedJacobianellipticfunctionsolutions,solitonsolutions,triangularfunctionsolutions.

简介：AnewtypeBoussinesqmodelisproposedandappliedforwavepropagationinawaveflumeofuniformdepthandoverasubmergedbarwithcurrentpresentorabsent,respectively.Firstly,forthepropagationofmonochromaticincidentwavewithcurrentabsent,theBoussinesqmodelistestedinitscompleteform,andinaformwithouttheintroductionofutilityvelocityvariables.Itisvalidatedthattheintroductionofutilityvelocityvariablescanimprovethecharacteristicsofvelocityfield,dispersionandnonlinearity.BothversionsoftheBoussinesqmodelsareofhigheraccuracythanthefully-nonlinearfourth-ordermodel,whichisoneofthebestformsamongtheexistingtraditionalBoussinesqmodelsthatdonotincorporatebreakingmechanisminonedimension.Secondly,theBoussinesqmodelinitscompleteformisappliedtosimulatingthepropagationofbichromaticincidentwaveswithcurrentpresentorabsent,respectively,andthemodeledresultsarecomparedtotheanalyticalonesortheexperimentalones.Themodeledresultsarereasonableinthecaseofinputtingbichromaticincidentwaveswiththestrongopposingcurrentpresent.

简介：ThenonlocalsymmetryoftheBoussinesqequationisobtainedfromtheknownLaxpair.Theexplicitanalyticinteractionsolutionsbetweensolitarywavesandcnoidalwavesareobtainedthroughthelocalizationprocedureofnonlocalsymmetry.Someothertypesofsolutions,suchasrationalsolutionsanderrorfunctionsolutions,aregivenbyusingthefourthPainlev′eequationwithspecialvaluesoftheparameters.Forsomeinterestingsolutions,thefiguresaregivenouttoshowtheirproperties.

简介：Inthispaper,weobtainthesolitonsolutionsforthe'good'Boussinesqequationonaconstantbackground.Basedontheasymptoticanalysisofthesolutions,wefindthatthisequationadmitsboththeelasticandresonantsolitoninteractions,aswellasvariouspartiallyinelasticinteractionscomprisedofsuchtwofundamentalinteractions.Viapicturedrawing,wepresentsomeexamplesofsolitoninteractionsonnonzerobackgrounds.Ourresultsenrichtheknowledgeofsolitoninteractionsinthe(1+1)-dimensionalintegrableequationwithasinglefield.

简介：借助Mathematics4.0软件、改进的广义幂指函数法研究了ModifiedImprovedBoussinesq方程,得到了方程的精确解,这种方法也适合研究其它的非线性发展方程.

简介：TheWahlquist-Estabrook(WE)prolongationstructuresofmodifiedBoussinesq(MB)systemarestudiedfromthecoveringspointofview.Therealizationsandclassificationsofone-dimensionalcoveringsofthissystemareobtainedcompletely.MoreoverthesufficientandnecessaryconditionsforavectorfieldtobeanonlocalsymmetryofthissystemarealsodemonstratedintheWEprolongationstructures.

简介：Inthispaper,weconsidertheglobalexistenceofsolutionsfortheCauchyproblemofthegeneralizedsixthorderbadBoussinesqequation.Moreover,weshowthatthesupremumnormofthesolutiondecaysalgebraicallytozeroas(1+t)(1/7)whentapproachestoinfnity,providedtheinitialdataaresufcientlysmallandregular.

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简介：Inthispaper,anewcompletelyintegrablesystemrelatedtothecomplexspectralproblem—φ_(xx)+(i/4)uφ_x+(i/4)(uφ)_x+(1/4)vφ=iλφ_xandtheconstrainedBowsoftheBoussinesqequationsaregenerated.AccordingtotheviewpointofHamiltonianmechanics,theEuler-LagrangeequationsandtheLegendretransformations,areasonableJacobi-Ostrogradskycoordinatesystemisobtained.Moreover,bymeansoftheconstrainedconditionsbetweenthepotentialu,vandtheeigenfunctionφ,theinvolutiverepresentationsofthesolutionsfortheBoussinesqequationhierarchyaregiven.

简介：TheHamiltonianformulationsofthelinear'good'Boussinesq(L.G.B.)equationandthemulti-symplecticformulationofthenonlinear'good'Boussinesq(N.G.B.)equationareconsidered.Forthemulti-symplecticformulation,anewfifteen-pointdifferenceschemewhichisequivalenttothemulti-symplecticPreissmannintegratorisderived.Wealsopresentnumericalexperiments,whichshowthatthesymplecticandmultisymplecticschemeshaveexcellentlong-timenumericalbehavior.

简介：本文通过阐述以映射法为主的几种代数方法的主要思想，说明了它们之间的关系及映射方法较其它方法的优越性，求得了变形Boussinesq方程的各种精确行波解。

简介：Theusual(1+1)-dimensionalSchwartzBoussinesqequationisextendedtothe(1+1)-dimensionalspace-timesym-metricformandthegeneral(n+1)-dimensionalspace-timesymmetricform.TheseextensionsarePainlevintegrableinthesensethattheypossessthePainlevproperty.Thesinglesolitonsolutionsandtheperiodictravellingwavesolutionsforarbitrarydimensionalspace-timesymmetricformareobtainedbythePainlev-Bcklundtransformation.

简介：WepresentanF-expansionmethodforfindingperiodicwavesolutionsofnonlinearevolutionequationsinmathematicalphysics,whichcanbethoughtofasaconcentrationofextendedJacobiellipticfunctionexpansionmethodproposedrecently.ByusingtheF-expansion,withoutcalculatingJacobiellipticfunctions,weobtainsimultaneouslymanyperiodicwavesolutionsexpressedbyvariousJacobiellipticfunctionsforthevariantBoussinesqequations.Whenthemodulusmapproaches1and0,thehyperbolicfunctionsolutions(includingthesolitarywavesolutions)andtrigonometricsolutionsarealsogivenrespectively.

简介：Inthispaper,westudytheCauchyproblemforthe3DgeneralizedNavier-Stokes-Boussinesqequationswithfractionaldiffusion:{ut+（u·▽）u+v∧2αu=-▽p+θe（3）,e3=（0,0,1）T,θt+（u·▽）θ=0,Dicu=0.Withthehelpofthesmoothingeffectofthefractionaldiffusionoperatorandalogarithmicestimate,weprovetheglobalwell-posednessforthissystemwithα≥5/4.Moreover,theuniquenessandcontinuityofthesolutionwithweakerinitialdataisbasedonFourierlocalizationtechnique.Ourresultsextendonesonthe3DNavier-Stokesequationswithfractionaldiffusion.

简介：我们在一半上为好Boussinesq方程学习一个initial-boundary-value问题线

简介：Ageneralmappingdeformationmethodispresentedandappliedtoa(2+1)-dimensionalBoussinesqsystem.Manynewtypesofexplicitandexacttravellingwavesolutions,whichcontainsolitarywavesolutions,periodicwavesolutions,JacobianandWeierstrassdoublyperiodicwavesolutions,andotherexactexcitationslikepolynomialsolutions,exponentialsolutions,andrationalsolutions,etc.,areobtainedbyasimplealgebraictransformationrelationbetweenthe(2+1)-dimensionalBoussinesqequationandageneralizedcubicnonlinearKlein-Gordonequation.

简介：采用变物性格子Boltzmann通量求解器（VPLBFS)研究了Rayleigh-Benard热对流.以超临界流体为例，采用VPLBFS的简化形式和标准形式分别得到了通常关注的基于Boussinesq假设的常物性解，只考虑部分物性变化的基于partialBoussinesq假设的PBA解，以及考虑流体全部物性变化的变物性解，分析了non-Boussinesq效应对Rayleigh-B6nard热对流的影响，讨论了不同温差条件下的non-Boussinesq效应.研究结果表明：non-Boussinesq效应对超临界流体的Rayleigh-B6nard热对流有非常显著的抑制作用，论证了在研究热对流时考虑流体全部物性变化的必要性.

简介：Aclassofperiodicinitialvalueproblemsfortwo-dimensionalNewton-Boussinesqequationsareinvestigatedinthispaper.TheNewton-Boussinesqequationsareturnedintotheequivalentintegralequations.Withiterationmethods,thelocalexistenceofthesolutionsisobtained.Usingthemethodofaprioriestimates,theglobalexistenceofthesolutionisproved.

简介：主要考虑1＋1维Boussinesq系统的一个Darboux变换,反复利用该Darboux变换,可以从该系统的一个已知解出发,通过代数运算和求导运算得到系统的新解.