广义(22b1)维KP-BBM方程和广义Camassa-Holm方程的行波解

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1、AbstractAbstractInthispaperwestudytwononlineardifferentialequations：(2+1)-dimensionalgeneralizedKP-BBMequationandgeneralizedCamassa-Holmequation.Byusingthesine-cosinemethodandtheextendedtanh-method,weobtaincompactonsolution,solitarypatternsolutionandperiodicsolutionofthe(2+1)

2、-dimensionalgeneralizedKP-BBMequation.ForgeneralizedCamassa-Holmequation,byusingthemethodofbifurcationtheoryofdynamicalsystemanddirectintegrationmethod,weobtainpeakon,cuspon,smoothsoliton,periodiccuspwavesolutionsinthecase2,obtainpeakon,loop,periodiccuspwavesolutionsinthec

3、ase3,andobtainunboundedwave,periodicwavesolutionsinthecase0．Inaddition,wegivevarioussufficientconditionstoguaranteetheexistenceoftheabovesolutionsanddiscussthetravelingwavesolutionbranchanddynamicbehaviorofthisequation．Thestructureofthepaperisorganizedasfollows：Thefirstc

4、hapter,wemainlytalkabouttheresearchbackgroundandresearchdevelopmentsofthe(2+1)-dimensionalgeneralizedKP-BBMequationandgeneralizedCamassa-Holmequation．Thesecondchapter,weintroducetheoverviewofsolitontheoriesandthesine-cosinemethod,theextendedtanh-methodmethod,themethodofbifurc

5、ationtheoryofdynamicalsystemwhichareappliedtothispaper．Thethirdchapter,wediscussthecompactonsolution,solitarypatternsolutionandperiodicsolutionofthe(2+1)-dimensionalgeneralizedKP-BBMequation．Thefourthchapter,westudythetravelingsolutionsandsolutionclassificationsofgeneralizedC

6、amassa-Holmequationforcases2,3and0．Thefifthchapter,wegiveasummarytothispaperandputforwardtotheresearchworkinthefuture．Keywords:(2+1)-dimensionalgeneralizedKP-BBMequation;GeneralizedCamassa-Holmequation;Bifurcationtheoryofdynamicalsystem;Singlepeaksoliton;Solitarywaves

7、olutionII万方数据目录目录摘要........................................................................................................................................IAbstract................................................................................................................

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