非線性數(shù)學(xué)物理中的對(duì)稱(chēng)和達(dá)布變換.pdf

1、寧波大學(xué)碩士學(xué)位論文非線性數(shù)學(xué)物理中的對(duì)稱(chēng)和達(dá)布變換姓名：胡曉瑞申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：陳勇20090413??????????SymmetryDarbouxTransfmationintheNonlinearMathmaticalPhysicsAbstractThesymmetrymethodDarbouxtransfmationarethepowerfultoolstosolvetheequationsinnonl

2、inearmathematicalphysics.FirstlywestudyedthetheiesmethodsofthesymmetrygroupreductionsincludingclassicalLiegroupmethodnonclassicalLiegroupmethodCKdirectmethodthemodifiedCKmethod.Basedonthesemethodsweinvestigatedanonispect

3、ralKPequation.SecondlyoneofthemainapplicationsofLietheyofsymmetrygroupsfdifferentialequationsistheconstructionclassificationofgroupinvariantsolutionswhichisinrelationtotheoptimalsystem.Inthisrespectweconsideredageneral(2

4、1)dimensionalnonlinearKleinGdonequation.LastlyafterstudyingtherelatedknowledgeofDarbouxtransfmationweconstructedabinaryDarbouxtransfmationfthemodifiedKPequation.Thethesisisarrangedasfollows:Chapter1Introduction.Severalme

5、thodsfobtainingexactsolutionsofthenonlinearmathematicalphysicsequationsareintroducedinthischapter.Chapter2SymmetryReductions.ThischapterintroducessomerelevantknowledgeaboutthesymmetryReductions.WemakeuseofCKdirectmethodt

6、heclassicalLiegroupmethodthemodifiedCKmethodtoinvestigatethesymmetryofanonispectralKPequationrespectively.Fromtheresultsonecanseethesimilaritiesdifferencesamongtheabovethreemethods.Chapter3SymmetryOptimization.Onecanmake

7、useofsymmetryoptimizationtoconstructgroupinvariantsolutionsitsclassification.Inthischapterweinvestigateageneral(21)dimensionalnonlinearKleinGdonequation.InaccdancewiththedimensionsofitsLiealgebraitisdividedintothreetypes

8、.Feverytypeweconstructitsgroupinvariantsolutionsthecrespondingonedimentionaloptimalsystemrespectively.Chapter4BinaryDarbouxTransfmation.ThischapterfirstlyintroducestherelevantknowledgeaboutDarbouxtransfmation.Thenweconst