高阶非线性薛定谔方程的精确解

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1、万方数据应用数学MATHEMATICAAPPLICATA2007，20(3)：505～511ExactSolutionstotheHigherOrderNonlinearSchr6dingerEquationPENGYan—ze(彭彦泽)，SHEN(DepartmentofMathematics，Huazhong430074，China)Ming(沈明)，WANGZuo．jie(王作杰)UniversityofScienceandTechnology，WuhanAbstract：Byusingthemodifiedmappingmethodandth

2、eextendedmappingmethod，wederivesomenewexactsolutionsofthehigherordernonlinearschr6dingerequation，whicharethelinearcombinationoftwodifferentJacobiellipticfunctions．Thesolutionsinthelimitcaseshavealsobeenstudied．Keywords：Exactsolutions；Higherordernonlinearschr6dingerequation；Modi

3、fiedmappingmethod；ExtendedmappingmethodCLCNumber：0175．25AMS(2000)SnbjectClassification：35Q51Documentcode：AArticleID：i001-9847(2007)03-0505—071．IntroductionInthestudyofnonlinearwaves，oneofthefundamentalobjectsisthetravellingwaveSO—lutionswhicharesolutionsofconstantfrommovingwith

4、afixedvelocity．Ofparticularinter—estarethreetypesoftravellingwave：thesolitarywaves，whicharelocalizedtravellingwavesasymptoticallyzeroatlargedistances；theperiodicwavesandthekinkwaves，whichriseordescendfromoneasymptoticstatetoanother．Investigationofsuchsolutionshasbeenahottopicof

5、researchforseveraldecades．Therearemanymethodsforfindingspecialsolutionstononlinemrevolutionequations．SomeofthemostimportantmethodsareB／icklundtransforma—tions[11，thealgebraicmethod[2

6、，tanhmethodE3'引，Jacobiellipticfunctionmethodanditsex—tensions[s，6

7、．theWeierstrassellipticfuncti

8、onmethodr7

9、andSOon．Recently，theexactperiodicwavesolutionsintermsoftheJacobiellipticfunctions；fornon-linearevolutionequationsattractconsiderableinterest．ThethreebasicJacobiellipticfunctionssn$一sn(八仇)，cn$一cn(八m)anddn$一dn(八m)，wherem(O

10、thewell—knowntypeoftrigonometricrelationssuchas：sn2拿+cn2车一1，dn2e—q-m2sn2搴一1，(sn搴)7一cnSdne，(cnO7一一snedng，(dnO7一一m2sn&畦．When优÷l，theJacobiellipticfunctionsdegeneratetothehyperbolicfunctions，i．e．*Receiveddate：December1，2006Biography：PENGYan-ze，male，Han，Hubei，professor，majorinnonlin

11、earevolutionequation．万方数据506MATHEMATICAAPPLICATA2007sn