應用Hirota雙線性方法求解若干耦合方程的怪波解.pdf

1、應用Hirota雙線性方法求解若干耦合方程的怪波解ApplyHirotabilineartosolvetheroguewavesofsomecouplingequations作者：孫艷波Author：翰nboSun指導教師：張翼專業(yè)：系統理論學位：理學碩士授予單位：浙江師范大學Supervisor：羔!圣壘壘望gMajor：璺Y璺主皇!里璺!墜竺Q!YDegree：—塵魚ster墮ScienceInstitute：圣墜魚i壘望g盟旦!婆

2、壘!望里i翌蘭曼i!zMay，2015AbstractSolutionoftheequationistheemphasesanddifficultiesofnonlinearpartialdifferen—tialequationisstudied，andthetheor37ofsolitonisalsoaresearchhotspot。Thispapermainlystudiesthetwot3，pesofintegrableequa

3、tion：thecouplingSchrbdinger——KdPequationandtheKJp—IIequationwithselfconsistentsources協’usingtheHirotabilinearmethodItisoftenusedfordirectl3’solvingsolitonsolutionandrationalsolutionofnonlinearpartialdifferentialequations

4、AccordingtodifferenttypesofequationWeusedthedifferemwaystoanalyzeequationFirstofall：bj’introducingnewfunctionspotentialequationtransformationwillbeconvertedtobilinearformAndweexpandthenewfunctiondisturbance，andmakeparame

5、terstotakelimitingThesecondwa、iconvertsbilinearequationto丁functionandtheformofastrangewavesolutionoftheoriginalequationisobtainedItwillchangetheshapeofroguewaveunderthedifferentparametersChapter2Onthebasisofthebilinearfo

6、rmofthecouplingSchrSdinger——KdVequation：theroguewavesolutionofthecouplingSchrSdingerKdVequationisderivedFirstl37ane職’variateisappliedandtheequationistransformedintodoublelinearequationThentheneⅥ’functionisunfoldedwithsom

7、eparametersTheroguewaveisobtainedthroughtakingthelimitoftheparametersChapter3ResearchismainlyfocusedontheroguewavesolutionsoftheKP—I1equationwithselfconsistentsourcesOnthebasisofthedoublelinearequationtheoriginalequation

8、istransformedintoequivalentequationcontainingnearvariablesbyvariablesubstitutionTherationalsolutionsareobtainedbyusingthe丁function，ThentheroguewavesolutionsoftheequationcanbederivedThefundamentalroguewavesandsecondorderr