广义Korteweg—de Vries方程的数值行波解-论文.pdf

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1、2014年12月阴山学刊Dec．2014第28卷第4期YINSHANACADEMICJOURNALV01．28No．4NumericalTravelingWaveSolutionfortheGeneralKorteweg—deVriesEquationGUOZhong——zhao(FacultyofMathematics，BaotouTeacher~College；Baotou014030)Abstract：Anewexponentialfinitedifferencemethodisconstructedandusedfors

2、olvingthegeneralKofleweg—deVries(KdV)equation．Someapproximatetravelingwavesolutionsareobtained．Comparisonsbetweennumericaltravelingwavesolutionsandtheexactsolutionsrevealtheefficiencyofthescheme．Keywords：GeneralKdVequation；Exponentialfinitedifferencemethod；Travelingw

3、avesolution中图分类号：O241．82文献标识码：A文章编号：1004—1869(2014)04—0005—061IntroductionThewe11knownKdVeauationhadbeenderivedin1885bythetwoscientistsKorteweganddeVriestode—scribelongwavepropagationonshallowwater．TheKdVandtheKdV—typeequationsnotonlyplayanimportantroleinsolitontheor

4、y．butalsorepresentVerygoodprospectinmanyappliedfieldssuchasfluid，mechanics，plas’mas，crystallatticevibrationsatlowtemperatures，etc．Duringthelastfewdecades，theconstructionofexactsolutionsforKdVandtheKdV—typeequationshasbeendonebvmanyresearchers．TheJacobianellipticfunct

5、ion，thepowerfulinversescatteringtransform，theBack—lundtransformati0nstechnique，thePainleveanalysis，theLiegrouptheoreticalmethod，thedirectalgebraicmeth-odandthetangenthyperbolicmethodhavebeenusedinconstructionofexactsolutionsofKdV—typeequations[卜Adomiandecompositionme

6、thodandfinitedifferencemethodhavebeenusedtofindnumericalsolutionofGK—．dVequationEm3HelalhavestudiedanalyticallyandnumericallysomephysicalproblemsthatleadtotheKdVe。．quationsandthes0litonsolutionshavebeenobtained[¨’．Exponentialfinitedifferencemethod(EFD)hasbeenusedtofi

7、ndthenumericalsolutionofKdVequation[”]。TheGeneralKorteweg—deVriesequation(GKdV)hasthefollowingform：¨￡+“+=0，(1)wherettn“andUrepresentthenonlinearconvectionanddispersioneffects．Inthisw0rk．weconstructanewExponentialfinite—difference(EFD)methodanduseittodiscussthenu‘meri

8、caltravelingwavesolutionsofGKdVequation．TheGKdVequationwediscussedispresentedbyEq·(1)·Specificexactsolutionwillbedeterminedforeachv