若干（2+1）維孤子方程的有限參數(shù)解.pdf

1、鄭州大學(xué)博士學(xué)位論文若干（21）維孤子方程的有限參數(shù)解姓名：吳勇旗申請學(xué)位級別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：曹策問20050916AbstractItisdifficultytogettheexplicitsolutionforthe(21)dimensionalsofitonequation。QuiteafewprogresshasbeenmadedmingtherecentdecadesNeverthelesseachmethodh

2、asitslimitationThepurposeofthepI柵tpaperisesingthenoniinearizationapproachtostudytheexplicitfiniteparametersolutiontothedifficult(21)dimensionalsofitonequationFour(21)dimensionalsofimnmodelsminvestigated：the(21)dimeIlsion

3、alsineGordonequation(SG)，twokindsofmodifiedKadomtsevPetviashviliequation(mKP)，a(21)dimensionalintegrableequationassociatedwithBoitiPempinelli—Tuspectralproblem(BET)Firstmrtingfmmthespectralproblemassociatedwiththesofimnm

4、odel，weconstructthefundamentalidentityandfindouttheLenartoperatorpairandtheexplicitexpressionoftheLeuart’SgradientsbyusingthecommutativeconditionfTomwhichthehierarchyof(11)dimensionalsolitonequationsisobtainedandtheinter

5、estingf21)dimensionalsolitonequationisconstructedbythecompatibleconditionoftwo(11)dimensiomlsofitonequationsThenthroughthenonlinearizationprocedme，allintegrablefinitedimensionalHamilmniansystemisacquiredwhosecompleteinte

6、grabilityinLiouvillesenseisprovedbyLaxmatrixandgenemtingfunctionoftheconservedintegralsThusahierarchyofintegrablefinitedimensionalHamiltoniansystemsisobtainedbywhichtheintegrabledecompositionofthe(21)dimensionalsolitoneq

7、uationisacquiredAsnnapplicationofalgebraicculNetheorytheellipticcoordinatesandtheAbebJacobicoordinatesareintroducedsuitably，fromwhichthestraighteningoutoftheHamiltonianflowsaremadeandthequadratureisobtaineddirectlyFinall