Symmetry Methods for Differential Equations.pdf

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1、SymmetryMethodsforDifferentialEquationsSymmetryisthekeytosolvingdifferentialequations.Therearemanywell-knowntechniquesforobtainingexactsolutions,butmostofthemaremerelyspecialcasesofafewpowerfulsymmetrymethods.Thesemethodscanbeappliedtodifferentialequationsofanunfam

2、iliartype;theydonotrelyonspecial"tricks."Instead,agivendifferentialequationcanbemadetorevealitssymmetries,whicharethenusedtoconstructexactsolutions.Thisbookisastraightforwardintroductiontosymmetrymethods;itisaimedatappliedmathematicians,physicists,andengineers.Thep

3、resentationisin-formal,withmanyworkedexamples.Itiswrittenatalevelsuitableforpost-graduatesandadvancedundergraduates.Thereadershouldbeabletomasterthemaintechniquesquicklyandeasily.Thistextcontainsseveralnewmethodsthatwillinterestthosewhoseresearchinvolvessymmetries.

4、Inparticular,methodsforobtainingdiscretesymmetriesandfirstintegralsaredescribed.PeterHydonisaLecturerinMathematicsattheUniversityofSurrey.CambridgeTextsinAppliedMathematicsMaximumandMinimumPrinciplesM.J.SEWELLSolitonsP.G.DRAZINANDR.S.JOHNSONTheKinematicsofMixingJ.M

5、.OTTINOIntroductiontoNumericalLinearAlgebraandOptimisationPHILIPPEG.CIARLETIntegralEquationsDAVIDPORTERANDDAVIDS.G.STIRLINGPerturbationMethodsE.J.HINCHTheThermomechanicsofPlasticityandFractureGERARDA.MAUGINBoundaryIntegralandSingularityMethodsforLinearizedViscousFl

6、owC.POZRIKIDISNonlinearWaveProcessesinAcousticsK.NAUGOLNYKHANDL.OSTROVSKYNonlinearSystemsP.G.DRAZINStability,InstabilityandChaosPAULGLENDINNINGAppliedAnalysisoftheNavier-StokesEquationsC.R.DOERINGANDJ.D.GIBBONViscousFlowH.OCKENDONANDJ.R.OCKENDONScaling,Self-Similar

7、ityandIntermediateAsymptoticsG.I.BARENBLATTAFirstCourseintheNumericalAnalysisofDifferentialEquationsA.ISERLESComplexVariables:IntroductionandApplicationsM.J.ABLOWITZANDA.S.FOKASMathematicalModelsintheAppliedSciencesA.C.FOWLERThinkingAboutOrdinaryDifferentialEquatio

8、nsR.O'MALLEYAModernIntroductiontotheMathematicalTheoryofWaterWavesR.S.JOHNSONTheSpace-TimeRayMethodV.M.BABICH,I.MOLOTKOVANDVS.BULDYREVRarefiedGas