Baldwin-Dissertation.pdf

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1、DISPERSIVESHOCKWAVEINTERACTIONSANDTWO-DIMENSIONALOCEAN-WAVESOLITONINTERACTIONSbyDOUGLASEUGENEBALDWINB.S.,ColoradoSchoolofMines,2003M.S.,ColoradoSchoolofMines,2004AthesissubmittedtotheFacultyoftheGraduateSchooloftheUniversityofColoradoinpartialfullfillmentoft

2、herequirementforthedegreeofDoctorofPhilosophyDepartmentofAppliedMathematics2013Thisdissertationentitled:Dispersiveshockwaveinteractionsandtwo-dimensionalocean-wavesolitoninteractionswrittenbyDouglasEugeneBaldwinhasbeenapprovedfortheDepartmentofAppliedMathem

3、aticsMarkJ.AblowitzKeithJulienThefinalcopyofthisthesishasbeenexaminedbythesignatories,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.Wefindthisasymptoticsolutionusingtheinversescatteringtr

8、ansform(IST)andmatched-asymptoticexpansions;wealsocompareitwithanumericallycomputedsolution.Whilemulti-stepdataevolvetohavemultiphasedynamicsatintermediatetimes,theseinteractingDSWseventuallymergetofor