一維Gross-Pitaevskii方程孤波解的計算研究.pdf

1、分類號024221學校代碼10542密級學號201202100837一維Gross—Pitaevskii方程孤波解的計算研究NemucialResearchonSolitonSolutionsofldGrossPitaevskiiEquation研究生姓名：劉云指導(dǎo)教師姓名、職稱：謝資清教授學科專業(yè)：計算數(shù)學研究方向：偏微分方程數(shù)值解湖南師范大學學位評定委員會辦公室二零一五年五月ABSTRACTWiththefurtherresearc

2、handdevelopmentofthesolitonphenomenon，theexistenceofsolitarysolutionshasbeenprovedincondensedmatterpaysicsS—incethesuccessfulrealizationoftheexperimentofBose—Einsteincondensation，manypaysicistsandmathematiciansareveryint

3、erestedinitOneofthemostpopularmathematicalmodelofdepictingtheBose—EinsteincondensationistheGross—Pitaevskiiequation(G—Pequation)Inspiredbythenumericalsim—ulationofsolitoninitialstateforsolitonwaveinlasertransmission，whic

4、hwasstudiedbyChuaamiaoChen，eta1，thispaperismainlyconcernedwiththesolitonsolutionsofthreekindsofG—Pequationwhosepotentialiszeropotential，opticallatticepotentialandharmonicpotentialrespectivelySolitarywaveisaspecialfluctua

5、ntform，howtoimitateitnumerciallyisverymeaningfulInthispaper，aSearch—extensionmethod(SEM)basedonChebyshevspectralcollocationapproachisadoptedtocalculatethesolitoninitialstatesofstationaryGross—PitaevskiiequationThen，witht

6、hesesolitoninitialstatesservingastheinitialvalues，weshalldiscusstheinitial—boundaryproblemoftheoriginaldynamicalG—PequationandfurtherinvestigatethebasicpropertiesofthesolutionFinally，inordertostudythetime—dependentevolut

7、ionofthesesolitoninitialstates，weproposeaconservativediscretescheme，whichcombinestheChebyshevspectralcollocationinspacewithrelaxationmethodintimeThenumercialresultsdemonstratethatthesesolitoninitialstatescanproducesolita