两个非线性方程新自backlund变换及精确解

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1、2一Withtherapiddevelopmentofnonlinearscience，findingtheexactsolutionsofthenonlinearevolutionequations(NLEES)becomesanimportanttopicinmathematicsandphysics．Atpresent,avastvarietyofdirectmethodsfindingtheexactsolutionsofNLEEShavebeenpresentedincludingthehomogeneousbalancemethod、Backlundtransform

2、ationmethod、HirotabilinearmethodandSOon．Asadirectmethod,thehomogeneousbalancemethodisveryeffectiveforfindingspecialexactsolutionsofNLEES．Specialexactsolutionsofmanynonlinearequationsinmathematicalphysicshavebeenobtainedbyusingit．Inrecentyears，therealetheextensionofthehomogeneousbalancemethoda

3、ndthemodifiedhomogeneousbalancemethod．Thispaperobtainsthenewauto-BacklundtransformationsandexactsolutionsoftwononlinearevolutionequationsbYusingthemodredhomogeneousbalancemethodthatisbased011thetheoriesofthehomogeneousbalancemethodandHirotabilinearmethod．Thispaperconsistsofthefollowingthreech

4、apters．InChapterl，webrieflyintroducethebackgroundandhistoryaboutthesolitontheoryandviewsomebasicmethodsseekingexactsolutionsforthenonlinearevolutionequationsaswellasthegeneralstepsbYusingthehomogeneousbalancemethodandthemodifiedhomogeneombalancemethod．Then,themajorworkofthispaperispresented．I

5、nChapter2，firstlyweobtainanewauto—BacldundtransformationofthegeneralizedBoussinesqequationbyusingthemodifiedhomogeneousbalancemethod．Theauto—Backlundtransformationonlyinvolvesonequadratichomogeneityequationwrittenasabilinearequation．Basedontheauto-Baekhmdtransformation,thetwo-solitonsolutiono

6、fthegeneralizedBoussinesqequationisobtainedbyusinge-expansionmethod．Then,asimplifiedversionofthemodifiedhomogeneousbalancemethodisgivenandtheauto-BacklundtransformationofthegeneralizedBoussinesqequationisre-derived．InChapter3，anewauto-BacklundtransformationandfourgroupsexactsolutionsoftheBoit

7、i—Leon-PempineUi(BLP)equationsalepresentedbyusingthemodifiedhomogeneousbalancemethod．Keywords：homogeneousbalancemethod；modifiedhomogeneousbalancemethod；thegeneralizedBoussinesqequatiomtheBoiti·Leon—Pempinelliequations：e1}【actsolution3一扬州大学硕士学