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：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：WeConsiderthefollowinginitlal-boundaryproblemofnonlinearSchrodingcr-BoussinesqeguationswithweaklydampnessinahoundeddomainΩofR^N:

简介：在关于k,hb,μb的非常弱的假设条件下,在Sobolev空间中证明了非齐次Dirichlet边界条件u=ud(x,y),(x,y)∈(e)Ω下非齐次椭圆型Boussinesq方程-（△）*(K(x,y)(u-hb)（△）u)=f(x,y,u),(x,y)∈Ω的解的唯一性以及齐次椭圆型Boussinesq方程（△）*(K(x,y)(u-hb)（△）u)=0,(x,y)∈Ω的解的存在性,其中Ω为有界多边形域.并给出反例,指出对一给定的f(x,y),非齐次方程-（△）*(K(x,y)(u-hb)（△）u)=f(x,y,u),(x,y)∈Ω的Dirichlet问题是不可解的.

简介：摘要：为了准确高效地模拟规则波浪生成与传播，在完全非线性Boussinesq数值水池框架下开发了一种基于流函数的造波技术。通过建立Boussinessq数值水池模型，利用Matlab软件编写流函数造波程序，实现了线性波数值造波，并将数值模拟结果与理论解进行对比，验证了流函数造波的可行性和准确性。同时，初步模拟了强非线性波浪的生成和传播，研究了强非线性波浪的传播特性。

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

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

简介：

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：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.