雙線性方法在幾類波動(dòng)方程中的應(yīng)用.pdf

1、浙江師范大學(xué)碩士學(xué)位論文雙線性方法在幾類波動(dòng)方程中的應(yīng)用姓名：葉靈婭申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：張翼20071226AbstractApplicationofBilinearMethodtoSomeWaveEquationsAbstractInthisdissertation，wemainlystudyHirotabilinearmethodtosomeaspectsinsolitonequations，especi

2、allytheaspectoffindingexactsolu—tionsThetopicsincludeseveralaspect：Constructingandsolvingthevariable—coefficientKPequationanditsintegrabilitysuchasBlicklundtransformation，nonlinearsuperpositionformulaandSOon；Derivationof

3、theN—solitonsolutionsintermsofWronskianandGrammiandeterminantforthevariablecoefficientKPequation；GeneralizationofHirotamethodtostudynewexactsolutionsofsomewaveequations，namelyperiodicwavesolutionsTofindexactsolutionstOso

4、litonequationsisallimportantaspectinsolitontheoryWecommencetheinvestigationontwoaspects：solutionsexpressedintermofHirota，WronskianandPfaffianandconstructionofexactsolutionsItisshownthatthebilinearmethodprovidesaverypower

5、fultoolinsearchingforexactsolutionsofsolitonequationsItalselatestheuniformityofsolitonequationswiththediversityofmethods，suchasHirotabilinearmethod，WronskiantechniqueandBiicklundtransforma—tionAccordinglyitexcavatesmoree

6、ssentialattributeofsolitonThespecificworkconsistsofthreeparts：e1)Inchapter2，wefirstpresentthedefinitionandelementarypropertiesofthebilinearoperatorsNext，wederivetheN—solitonsolutionsforthevariable—coefficientKPequationin