非等譜孤子方程與具自容源mKP方程的精確解.pdf

1、F癆醪j≯_I≥j≮參i：≥爹0≥j≤豢i。i。|鎏l：一iI。。j。一。j。。：17Ij0oo|一一一：、套≯l一奠I一i二，。，一7AbstractInthispaper，weconsiderthesolutionsofSomenonisospectralsoUtonequationsandthemKPequationwithselfconslstentsourcl葛byHirotamethod，bilincarB缸klundtra

2、nsformation，DarbouxtransformationandWronskiantechniquehChapland3weconsiderthenonisospectralandvariablecoemcientKdvandKPequationsbyHirotamethod，bilinearB置cklundtrans丘omationandWronskiantechnique，InChap2，westudythenonisosp

3、ectralKPequationbyDarbonxandbilinearBidklundtransformationWealsoanalyzenonisespectralcharacteristicsoftheobtainsolutionsSolutionsintheHirotasformandinWronskianformaredifferentbothformallyandessentiallyThesetwokindsofsolu

4、tionsarenotsameforrecoveringtheNsolitonsolutionsfmmthetransformationsTothenoniscepectralsolitonequationstheobtainsolutionstravelwithtimevaryingshapeandspeedItisworthwhiletomentionthatDarbotlx㈣tionandbifinearBickinndtrans

5、formationareautoBSEdundtransformationsfortheiscepectralsolitonequations，butthesedonottrueforthenoulsospectralsolitonsequationAsamatteroffacttheytransformollenoniscepectralsolitonequationtoanotherhChap4，fromthelinearprobl

6、emofmKPequation，wecanderivethemKPequationwithselfconsistent80urce8Ontheotherhand，wealsohopetofindthemultbsolltonsolutionsofthemKPequationwithselfconsistentsort_teesthroughHirotamethodandWronskiantechniqueThesetwodirectme

7、thodsbothdependonthebilinearformsoftheevolutionequationsWefirstpresentasetofdependentvariabletransformationstowriteoutthebillnearformofthemKPequationwithselfconsistentsourcesbywhlchwecallderiveone，two，eventhreesolitonsol

8、utionssuccessivelythroughthestandardHirota’8approachTheseresultscanhelp118tofindoutthetimeevolutioneasilyandconjectureageneralformulawhichdenotesNsolitonsolutionbutisonlyconjecturedandnotverifiedNext，withthehelpofthemess

9、ageOilthetimeevolutionobtainedbyme刪ofHirotamethodwecanconstructaWronskianandtrytoverifyittosatisfytherelatedbilinearequationsSincethereiBanonlinearterm(1edtobytheconcernedsource)inthetimeevolutionwehavetodevelopsolDtenov

10、eldetermiuantalidentiti糟andemployBomespecialtreatmentswhich啪di矗erentfromtheknownstandardWronskiantechnique80thatwe鋤finishtheWmnskianverificationsFinallywepresentaprocesstoshowthatthesolutionsofthebilinearequationsobtaine