1、大連理工大學(xué)碩士學(xué)位論文一類非線性偏微分方程若干求精確解方法的研究姓名：曾昕申請學(xué)位級別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：張鴻慶20050316SomeProblemsinNonlinearPartialDifferentialEquations’ExactSolutionsAbstractInthisdissertation，byapplyingtheideasofthemathematicsmechanization，underthei

2、nstructionoftheAC=BDtheoryofProfessorZhangHongqing，considerssomemethodsseekingexactsolutionsforthenonlinearpartialdifferentialequation(s)arisingfromthefieldsoffluidmechanics，aerodynamics，plasmaphysics，biophysicsandchemic

3、alphysicsChapter1ofthisdissertationisdevotedtoinvestigatingthetheoryandapplicationofmathematicsmechanization；ReviewingthehistoryanddevelopmentofthesolitontheoryandtheconstructionoftheNonlinearpartialdifferentialequation，

4、InadditionsomeachievementsonthesubjectdomesticandabroadarepresentedChapter2concernstheconstructionofexactsolutionsofnonlinearpartialdifferentialequation(s)undertheuniformframeworkofAC=BDtheoryThebasictheoryandapplication

5、aboutAC=BDmodelandtheconstructionoftheoperatorsofCandDareintroducedChapter3isdevotedmainlytogeneralizedalgebraicmethod，whichisadirectmethodthegeneralizedalgebraicmethodisshOwntosolve(21)dimensionaldispersivelongwaveequat

6、ions，andwhicilcanobtainabundantexactsolution(includingsolitarysolutions，solitonlikesolutions，periodicsolutions，periodiclikesolutionsandrationalsolutions)ofnonlinearpartialdifferentialequation(s)Chapter4mainlydealswiththe

7、PalnlevepropertyandBackhindtransformationofnonlinearpartialdifferentialequationTilegeneraltheoryofPalnlevesingularanalysisisdiscussed，(21)dimensionalBoussinesqequationlsPainlevepropel’tyisshowntopassthePainlevetestbyusin

8、gWTCmethod，anditsBacklundtransformationisobtainedthrougtlPainlevetruncatingexpansion；Backlundtransformationisdiscussedsimplyandisfurtherexpanded，(21)dimensionalBoussinesqequationlsabundantexactsolution(includingsolitonli

9、kesolutions，rationalsolutions)isobtainedbyreplacingtheseedsolutionwithunknownfunctionKeywords：Mathematicsmechanization；Soliton；Nonlinearpartialdifferentialequation；AC=BDtheory；C—Dpair；Exactsolution；BaCklundtransformation