广义的hirota_satsum_省略_合kdv系统的精确行波解_英文_王晓民

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1、内蒙古工业大学学报JOURNALOFINNERMONGOLIA第32卷第1期UNIVERSITYOFTECHNOLOGYVo1．32No．12013文章编号:1001－5167(2013)01－0002－05TheExactTravellingWaveSolutionsoftheGeneralizedHirota－SatsumaCoupledKdVSystemWANGXiaomin，SUDAOBilige(CollegeofSciences，InnerMongoliaUniversityofTechn

2、ology，Hohhote，010051，China)Abstract:Inthispaper，withtheaidofsymboliccomputationsystemMathematica，wesuccessfullyobtainedabundantexacttravellingwavesolutionsforthegeneralizedHirota－SatsumacoupledKdVsystembyusingthe(G'/G)－expansionmethod．Thetravelingwaveso

3、lutionsareexpressedbythreetypesoffunctionswhicharethehyperbolicfunctions，thetrigonometricfunctionsandtherationalfunctionswithtwoarbitraryparameters．Keywords:The(G'/G)－expansionmethod;Exacttravellingwavesolutions;ThegeneralizedHirota－SatsumacoupledKdVsys

4、temCLCnumber:O175．29Documentcode:A1IntroductionTherearemanydifferentmethodsusedforlookingexactsolutionsofnonlinearevolutionequations［1］［2］［3］(NLEEs)．Weknowtheinversescatteringmethod，theDarbouxtransform，theHirotabilinearmethod，［4］［5，6］［7，8］thehomogeneous

5、balancemethod，thetanhfunctionmethod，theauxiliaryequationmethod，thedirect［9］［10］algebraicmethod，theimprovedprojectiveRiccatiequationsmethod，theextendedsimplestequation［11］［12］method，the(G'/G)－expansionmethod，andsoon．Recently，Wangetal．introducedamethodasa

6、kindofauxiliaryequationmethod，calledthe(G'/G)－［12］expansionmethod，toobtainexacttravellingwavesolutionsforagivenNLEEs．Theauxiliaryequationusedinthismethodislinear，constantcoefficientsordinarydifferentialequation(ODE)．Henceitcanbesolvedeasilybythemanyknow

7、nmethods，suchascharacteristicsvaluemethod．Byusingthe(G'/G)－expansionmethod，manyauthorssuccessfullyobtainedmoreexacttravellingwavesolutionstoalargenumberof［12］－［14］［15］－［18］NLEEs．Later，themethodwasimprovedtofindmoretypesexactsolutions．Thepaperisarrangeda

8、sfollows．InSection2，weapplythe(G'/G)－expansionmethodtothegeneralizedHirota－SatsumacoupledKdVsystem．InSection3，someconclusionsaregiven．1112vt+vxxx+3uvx=0，wt+wxxx+3uwx=0，ut－uxxx－3uux－3(w－v)x=0．(1)2242ThegeneralizedHirota－Satsumacou