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1、具有三个位势的广义耦合无色散可积方程的多孤子解（英文）2O11年5月第42巷第3期内蒙古大学(自然科学版)JournalofInnerMongoliaUniversity(NaturalScienceEdition)May2011Vo1.42No.3ArticleID:1000—1638(2O11)03—0253-05Multi—solitonSolutionsoftheGeneralizedDispersionlessIntegrableEquationwithThreeCoupledPotentialsZhaqilao(C0llegeofMathema
2、ticsScience,InnerMongoliaNormalUniversity,Hohhot010022,China)Abstract:AnewN—foldDarbouxtransformationofthegeneralizedcoupleddis—Dersionlessintegrableequationisderivedwiththeaidofthegaugetransforma—tionbetweencorresponding2×2matrixspectralproblemswiththreepoten—tla1s.Asanapplicatio
3、noftheDarbouxtransformation,N—solitonsolutionsofthegeneralizedcoupleddispersionlessintegrableequationareexplicitlygiven.Keywords:Darbouxtransformation;solitonsolution;coupleddispersionlessinte—grableequationCLCnumber:O175.2Documentcode:AIntr0ducti0nThestudvofdispersionlesshierarch
4、iesisoneofthemostprominentsubjectinthefieldofnon—linearscience,partlybecauseofdispersionlessequationsemergenceindiverseareasofmathematicalandthe.retica1Dhysicssuchasquantumfieldtheory,conformalfieldtheory,stringtheory,solitontheorv,etc.Inpast,thecoupleddispersionlessequationandits
5、generalizationhasalsoattractedareatdealofinterestbecauseofitsniceintegrabilitystructureandsolitonsolutions.InRefs.[1—2],KonnoandKakuhataconsideredthegeneralformofthecoupleddispersionlessintegrableequation(CDIE)q+(rs)=0,,.一2r一0,s一25g一0(1)andobtainedthesingleanddoublesolitonsolution
6、sofCDIE(1)bytheinversescatteringtransform(IST).CDIE(1)hastwospecialcases:r=andr—.Theformercasewasfoundtobeequivalenttothesine—Gordone0uation[.andthelattertothePohlmeyer—gund--Reggeequation们.Forr—s,CDIE(1)reducestothemodelwithtwopotentials.Inthepastyears,manyeffortshavebeendedicate
7、dtothereducedequationandrichfamiliesofexactanalyticalsolutionshavebeenobtainedbvvari.useffectivemethods,suchasIST,Painlev6analysis∞,B/icklundtransformation(BT)"andDarbouxtransformation(DT)C783.However,toourknowledge,verylittleresearchhasbeendoneonCDIE(1)viatheN—foldDTmethod.Theaim
8、ofthispaPeristoobtainN—solitonsol
