應(yīng)用擴展的F—展開法求解一類非線性偏微分方程.pdf

1、江蘇大學(xué)碩士學(xué)位論文應(yīng)用擴展的F—展開法求解一類非線性偏微分方程姓名：張風(fēng)云申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：蔡國梁20071207江蘇大學(xué)碩士學(xué)位論文ABSTRACTInthispaperthemajorcontentsconclude：underHomogeneousbalanceideabytaking觚ladvantagesofF—expansionmethodandRiccatiequationinseekingexa

2、ctsolutionsofnonlinearPDEs，amodifiedF—expansionmethodisusedsolvingthecoupledSchrfdingerBoussinesqequationsandthedispersivedissipativeequationSimultaneouslyweproposedageneralizedmodifiedF—expansionmethodThemethodCanbeconv

3、enientlyoperated晰ththeaidofcomputersymbolicsystems(Mathematica)，andrichfamiliesofexactsolutionsofnonlinearPDEshavebeenobtained，includingsoliton—likesolutions，trigonometricfunctionsolutionsandrationalsolutionsByusingtheme

4、thod，wehavesolvedthecoupledMKdVequationsMassiveexactsolutionsofthemhavebeenobtained，andsomeofthesolutionsarenewWealsoprovidedsomefiguresofpartialsolutionsfordirectviewinganalysisFirstlyweresearchedtheexactsolutionsofthed

5、ispersivedissipativeequationbyusingthemodifiedFexpansionmethodSeveralclassesofexactsolutionsforthedispersivedissipativeequationareobtainedSolitarywavesolutionsbelongtotheseclassesByusingMathematicasomefiguresofpartialsol

6、utionsareprovidedfordirectviewinganalysisNext，weresearchedtheexactsolutionsofcoupledSchr6dingerBoussinesqequationsbyusingthemodifiedF—expansionmethodRichfamiliesofexactsolutionsofthemhavebeenobtained，includingbellshapeds

7、olitarysolutions，kinksolutions，soliton—likesolutions，complexsolutions，rationalsolutionsandSOonAndsomeofthemarenewWeconsiderthesesolutionswillmakesenseforexplainingsomephysicalphenomenonFinallyweintroducedageneralizedmodi

8、fiedFexpansionmethodandresearchedtheexactsolutionsofthecoupledMKdVequationsweobtaineditskinksolutions，soliton—likesolutions，complexsolutions，rationalsolutionsandSOonThisworkwillbeusefulforfurtherresearchtotheequationKEYW