帶弱阻尼的二維非線性Schrodinger方程有限差分格式的長時間性態(tài).pdf

1、黑龍江大學碩士學位論文帶弱阻尼的二維非線性Schrodinger方程有限差分格式的長時間性態(tài)姓名：王立剛申請學位級別：碩士專業(yè)：基礎數(shù)學微分方程數(shù)值解指導教師：張法勇2003.6.9英文摘要AbstractThetwodimensionalnonlinearSchrSdingerequationwithweaklydampedthatpossessesaglobalattractorisconsideredTheexistenceofa

2、nattractorisoneofthemostimportantcharacteristicsforadissipativesystem，Thelong—timedynamicsiscompletelydeterminedbytheattrac—totofthesystemAtpresent，moststudiesarelinkedtothesemi—discreteschemeandtheonedimensionalspatialv

3、ariableButthereareveryfewstudiesaboutthefull—discreteschemeandthehigherdimensionalspatialvariableFurthermore，theformerc2Ln’tbeextendeddirectlytothelatterAstheresult，thelatterisfocusedbythereseachersnowadaysThedy—namicMpr

4、opertiesofthediscretedynamicalsystemwhichisgeneratedbyafinitedifferenceschemeareanalysed，andtheexistenceofaglobalattractorforthediscretedynamicalsystemisprovedInordertoprovetheexistenceofanattractor，wefirstsetsuptheinter

5、polationunequalityintwodimensionalspace，fromwhich，thesimutaneousrelationofpbetween”怯and111isderivedThen，itconstructsthefinitediffer—enceschemeoftheequationandfromwhichestablishsthefunctional玩anditsrecursionrelationinthes

6、paceofH2functionsThereforetheex—istenceofanabsorbingsetinthespaceolH2functionsisdrawnFinally，theexistenceofanattractoroftheequationintwodimensionalspaceisobtainedbyusingtheconclusionin【3】keywords：NonlinearSchrOdingerequa