应用扩展的F-展开法求解一类非线性偏微分方程

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1、江苏大学硕士学位论文应用扩展的F—展开法求解一类非线性偏微分方程姓名：张风云申请学位级别：硕士专业：应用数学指导教师：蔡国梁20071207江苏大学硕士学位论文ABSTRACTInthispaper,themajorcontentsconclude：underHomogeneousbalanceidea,bytaking觚ladvantagesofF—expansionmethodandRiccatiequationinseekingexactsolutionsofnonlinearPDEs，amodifiedF—expansionmethodisusedsolvingthec

2、oupledSchrfdinger-Boussinesqequationsandthedispersivedissipativeequation．SimultaneouslyweproposedageneralizedmodifiedF—expansionmethod．ThemethodCanbeconvenientlyoperated晰ththeaidofcomputersymbolicsystems(Mathematica)，andrichfamiliesofexactsolutionsofnonlinearPDEshavebeenobtained，includingsol

3、iton—likesolutions，trigonometricfunctionsolutionsandrationalsolutions．Byusingthemethod，wehavesolvedthecoupledMKdVequations．Massiveexactsolutionsofthemhavebeenobtained，andsomeofthesolutionsarenew．Wealsoprovidedsomefiguresofpartialsolutionsfordirect-viewinganalysis．Firstly,weresearchedtheexact

4、solutionsofthedispersivedissipativeequationbyusingthemodifiedF-expansionmethod．Severalclassesofexactsolutionsforthedispersivedissipativeequationareobtained．Solitarywavesolutionsbelongtotheseclasses．ByusingMathematicasomefiguresofpartialsolutionsareprovidedfordirect-viewinganalysis．Next，weres

5、earchedtheexactsolutionsofcoupledSchr6dinger-BoussinesqequationsbyusingthemodifiedF—expansionmethod．Richfamiliesofexactsolutionsofthemhavebeenobtained，includingbell-shapedsolitarysolutions，kinksolutions，soliton—likesolutions，complexsolutions，rationalsolutionsandSOon．Andsomeofthemarenew．Wecon

6、siderthesesolutionswillmakesenseforexplainingsomephysicalphenomenon．Finally,weintroducedageneralizedmodifiedF-expansionmethodandresearchedtheexactsolutionsofthecoupledMKdVequations．weobtaineditskinksolutions，soliton—likesolutions，complexsolutions，rationalsolutionsandSOon．Thisworkwillbeuseful

7、forfurtherresearchtotheequation．KEYWORDS：NonlinearPDEs，homogeneousbalanceprinciple，themodifiedgeneralizedF—expansionmethod，exactsolutionslI学位论文版权使用授权书本学位论文作者完全了解学校有关保留、使用学位论文的规定，同意学校保留并向国家有关部门或机构送交论文的复印件和电子版，允许论文被查阅和借阅。本人授权江苏大学可以将本学位论文的全部内容或部分内容编入有