雙線性方法在孤子方程求解中的應用.pdf

1、遼寧師范大學碩士學位論文雙線性方法在孤子方程求解中的應用姓名：郭婷婷申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：張玉峰20090601AbstractContent：Thisdissertationhasmainlydonethefollowingfouraqpectsresearch：First，TheHirotabilinearmethodisdiscussedandthebriefapplicationofitisintroduce

2、d；Then，theWronskiantechniqueisintroducedtothe(21)dimensionalKdVequationandtheWronskiansolutionsandtheGrammiansolutionsofthesolitonequationaregenerated；BasedontheJacobiidentityakindofmethodofgeneratingLiealgebraisobtained

3、bytakingadvantageofalowdimensionLiealgebra；Intheend，byapplyingthePfaffianizationproceduretothe(21)dimensionalKdVequation，anewintegrablesystemwithPfaffiansolutionsisgeneratedThestructureofthispaperisasfollows：Chapter1isco

4、ncernedwiththeexpositionofthedevelopmentandtheresearchsituationofseveralsubjectswhichwillbediscussedinthispaperThemainresultsofthisdissertationarebrieflyintroducedinthischapterChapter2reviewthebilinearsolutionandexplaint

5、hebriefapplicationsChapter3，basedontheintroductionofWronskiansolutionsandGrammiansolutions，wegetthesolutionsofthe(21)dimensionalKdVequationandpopularizeitAkindofmethodsofgeneratingLiealgebraisobtainedbytakingadvantageofa