非線性微分差分方程守恒律的自動(dòng)推導(dǎo)研究.pdf

1、華東師范大學(xué)碩士學(xué)位論文非線性微分差分方程守恒律的自動(dòng)推導(dǎo)研究姓名：朱嬌鋒申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：計(jì)算機(jī)應(yīng)用技術(shù)指導(dǎo)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