資源描述：
《Baldwin-Dissertation.pdf》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。
1、DISPERSIVESHOCKWAVEINTERACTIONSANDTWO-DIMENSIONALOCEAN-WAVESOLITONINTERACTIONSbyDOUGLASEUGENEBALDWINB.S.,ColoradoSchoolofMines,2003M.S.,ColoradoSchoolofMines,2004AthesissubmittedtotheFacultyoftheGraduateSchooloftheUniversityofColoradoinpartialfull?llmentoft
2、herequirementforthedegreeofDoctorofPhilosophyDepartmentofAppliedMathematics2013Thisdissertationentitled:Dispersiveshockwaveinteractionsandtwo-dimensionalocean-wavesolitoninteractionswrittenbyDouglasEugeneBaldwinhasbeenapprovedfortheDepartmentofAppliedMathem
3、aticsMarkJ.AblowitzKeithJulienThe?nalcopyofthisthesishasbeenexaminedbythesignatories,andweFindthatboththecontentandtheformmeetacceptablepresentationstandardsOfscholarlyworkintheabovementioneddiscipline.Baldwin,DouglasEugene(Ph.D.,AppliedMathematics)Dispersi
4、veshockwaveinteractionsandtwo-dimensionalocean-wavesolitoninteractionsDissertationdirectedbyProfessorMarkJ.AblowitzManyphysicalphenomenaareunderstoodandmodeledwithnonlinearpartialdifferentialequations(PDEs).Unfortunately,nonlinearPDEsrarelyhaveanalyticsolut
5、ions.ButperturbationtheorycanleadtoPDEsthatasymptoticallyapproximatethephenomenaandhaveanalyticsolutions.AspecialsubclassofthesenonlinearPDEshavestablelocalizedwavescalledsolitonswithimportantapplicationsinengineeringandphysics.Thisdissertationlooksattwosuc
6、happlications:dispersiveshockwavesandshallowocean-wavesolitoninteractions.Dispersiveshockwaves(DSWs)arephysicallyimportantphenomenathatoccurinsystemsdominatedbyweakdispersionandweaknonlinearity.TheKortewegdeVries(KdV)equationistheuniversalmodelforphenomenaw
7、ithweakdispersionandweakquadraticnonlinearity.Hereweshowthatthelong-timeasymptoticsolutionoftheKdVequationforgeneralstep-likedataisasingle-phaseDSW;thisDSWisthe‘largest’possibleDSWbasedontheboundarydata.We?ndthisasymptoticsolutionusingtheinversescatteringtr
8、ansform(IST)andmatched-asymptoticexpansions;wealsocompareitwithanumericallycomputedsolution.Whilemulti-stepdataevolvetohavemultiphasedynamicsatintermediatetimes,theseinteractingDSWseventuallymergetofor
