1、華東師范大學碩士學位論文非線性微分差分方程守恒律的自動推導研究姓名：朱嬌鋒申請學位級別：碩士專業(yè)：計算機應用技術指導教師：柳銀萍20091001AbstractInthefieldofcontemporarynonlinearscience，theintegrabilityofnonlinearequationsattractsmuchattentionofresearchersWiththewell—knownWu’Seliminat
2、ionmethodandthecomputeralgebraicsystemMaple，westudyvariousalgebraicalgorithmsofcon—servationlawstononlineardifferentialdifferenceequation(DDE)andautomatedderivationOurmainworkincludesthefollowingthreepartsInPartI，wefocus
3、onfourtypicalalgorithmsforconstructinginfiniteconservationlawstothefamilyofdiscreteisospectralevolutionequationsin(11)一dimensionsThesemethodscontainRicattiequationmethod，characteristicfunctionformalsolutionmethod，multi—s
4、ystemtraceidentitymethodandB；icklundtransformmethodPartIIisdevotedtostudyingintegrabilityofnonlinearDDEsfromtheviewofcon—servationlawstartingfromscalingsymmetryThe“divideandconquer’strategyisusedtoimprovethekeystepsofthe
5、undeterminedcoefficientalgorithmforconstructingpoly—nomialconservationlawsofnonlinearDDEs，SOthecalculationcomplexityproblemcausedbythedramaticincreaseofredundancyissolvedFurthermore，Wu’Selimina—tionmethodisappliedtosolve
6、theobtainednonlinearalgebraicequationsthustogetamoreefficientalgebraicalgorithmInaddition，thediscreteEuleroperatorandhomotopyoperatoroforderzeroalepreliminarilystudiedPartIIIisdevotedtogivingthecorrespondingimplementatio
7、nsoftwarepackageCLawDDEsbasedontheimprovedalgebraicalgorithminMapleAslongasthesys—temoffirstorderpolynomialDDEsin(11)一dimensionsisgiven，nomatterwhetherasingleequationorthecoupledequation，CLawDDEsCanautomaticallyoutputthe
8、seal—ingsymmetriesofthevariablesandaseriesofpossiblepolynomialconservationlawsfordifferentrankForexponentialfunctionequationsandtriangularfunctionequationsetc，CLawDDEscanalsobeutilizedtoconstructtheconservationlawsafterp
9、ropervariablesubstitutionForparameterizednonlinearDDEs，thesoftwareisabletoautomaticallyfilterouttheparameterconstraintstoguaranteeintegrabilitySOastogetsomenewinte—grablesystemsKeywords：differential—differenceequation，co
