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1、©aÒO3—?úmUDCÆ“è11646Ø©K8:AKNSXÚ%Å9Ù36NåÆ¥A^ÆÒ:13010810026¶:áö;’¶¡:ó§åÆÆ:Åó§†åÆÆ•“:¬ïÄ•“:å§tÇØ©JFÏ:2018c115FADissertationSubmittedtoNingboUniversityfortheDoctorofPhilosophyDegreeRoguewaveoftheAKNSsystemanditsapplicationsin
uidmechanicsPh.D.Candidate:Li
2、hongWangSupervisor:ProfessorJiWangSupervisor:ProfessorJingsongHeFacultyofMechanicalEngineering&MechanicsNingboUniversityNingbo315211,ZhejiangP.R.ChinaDate:January15,2018wÅŒÆƬÆØ©Á‡°%Å´3°¹éÐœ¹eâ,Ñyážm•3ŒÌÅL"<‚¡ù«Å5ÃlÃK",•Ò´`éJýÿ"w,,°%Åé°þÊ1E•ÚïÓ(k4Œ»€5"3{¤
3、þ,°%Å•—Ø•Œ°J¯"Ïd,°%؆´EÍïE!°ÅL!°ó§!°/³•¡•‡ïÄ‘K"2007cÔnÆ[Ù*ÿ1Æ%Å,ù4Œ/íÄ%Å31Æ!lfN!6NåÆ+•¥ïÄ"d,ïÄ°%ÅI‡l6NåÆ•§Ñu"Ïd§6NåÆ•§ég,/¤%ÅïÄ•‡‘Kƒ˜"š‚5Ž™•§(NonlinearSchr•odingerequation,NLS)´•@uyk%Å)6NåÆ•§"C10c5§NLS•§%Å)õg31ÆÚ6NåÆ¢¥*"ù•‡(Jr¦©±Ablowitz-K
4、aup-Newell-Segur(AKNS)XÚ¥ž˜Û•)Š•.5ïÄ6N¥%Å,¿‰Ñ†ƒéA1Å"©ÄklAKNSXÚ1˜‡š²…6,=NLS•§Ã,Ïé%ÅÑy^‡!ëê!žÅ,•3˜„œ¹e%ÅýÿJønØÄ:"Äuù˜g´,©3NLS•§¥Úòzpáf)(=b-positon),‰Ñnb-positon1ªL«"©¥Ð«áf%ÅV•òzL§,¿JÑÏLÿþb-positonƒpŠ^«•Å/5*ÿp%Å•Y"X,
5、^“ê•{î‚y²NLS•§n%Å3ÙĪep
6、Ý•(2n+1)c,ùpc´%ÅìC²¡pÝ"duNõÔny–I‡ïákü‡½õ‡©þÅÄ.^±`²ØÓª!ªÇ½4z;,,••kõ©þXÚâUlnØþ)º˜õ‡Ôn
7、ƒmUþ†"Ïd,©±©þÚn©þNLS•§(=AKNS6)Ú?KdV•§(modiedKorteweg-deVriesequation,mKdV)(=AKNSn6)•~5ïÄõ©þAKNSXÚ"•XÚ/ïÄõ©þNLSÚõ©þmKdV%Å)¤^‡Úëê,©¥éõ©þXÚˆÙC†(DarbouxTransformation)
8、lü•¡?1U?:1)A¼êE¥Úƒ²£ÝT0;2)‰ÑA¼ê30NCÐm©)5Æ"ùp0´áf)kn)(½Œkn)).:"ÄuþãéˆÙC†U?,©‰Ñ©þNLSnŒkn)Úkn)1ªL«,Ù¥kn)=•%Å)"©¥?˜ÚòEÚ¦)©þkn)nØ9•{í2n©þÚn6,¿dd˜#ª9Ù•½5©Û"ÄuþãˆÙC†U?1˜:,3
9、^U?ˆÙC†Eõ©þNLSÚmKdV•§%Åž,©¥XÚ/‰ÑUEÑkn)“ê^‡,ù“ê^‡†½mû½ØÓÔnXÚe%Å)¤Ú
10、››Ônëê,ùé3Ôn¢¢y%ÅkX•‡•Š^"ÄuþãˆÙC†U?1:,uyõ©þNLSÚmKdV•§kn)©1¥õ‘ªgê5Æ"d5ÆŒ8BÑN©þnkn)Ñlõ‘ªgê5Æ,•ºXü©þœ¹"'…c:AKNSXÚ,ˆÙC†,áf,áf,%Å-I-AKNSXÚ%Å36NåÆ¥A^RoguewaveofAKNSsystemanditsapplicationin
uidmechanicsAbstractRoguewaveisthewavethatsuddenlyappearsintheocea
11、nevenundergoodmarinecondi-tion,whichexistsmomentlyandhastremendousamplitude.Peopleusuallysaythatthiswaveappearingfromnowhereanddisappeari