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dc.contributor.advisorYıldız, Aslı
dc.contributor.authorKar, Nurdan
dc.date.accessioned2018-09-13T07:05:19Z
dc.date.available2018-09-13T07:05:19Z
dc.date.issued2018
dc.date.submitted2018-06-01
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dc.identifier.urihttp://hdl.handle.net/11655/4894
dc.description.abstractIn this thesis, it is studied how the B¨acklund transformations of nonlinear partial differential equations are obtained and deriving new solutions from the known solutions by using these transformations with the superposition formulas obtained via the permutability conditions of the equations. Particularly, for some nonlinear partial differential equations which are well known in mathematical physics, the importance of B¨acklund transformations is emphasized by showing that one can derive N-solitons from 1-soliton solutions. For this purpose, Hirota D-operator and Hirota method that are used to obtain B¨acklund transformations are also explained. Within this context Korteweg-de Vries (KdV), Sine-Gordon (SG) and Boussinesq equations are analyzed in detail.tr_TR
dc.description.tableofcontentsÖZET ABSTRACT TEŞEKKÜR İÇİNDEKİLER DİZİNİ ŞEKİL LİSTESİ 1 GİRİŞ 2 Hirota Metodu 2.1 Hirota D-Operatörü 2.2 Hirota Pertürbasyonu ve Soliton Çözümler 3 Backlund Dönüşümleri 4 Korteweg-de Vries (KdV) Denklemi 4.1 KdV Denklemi İçin Miura Dönüşümü 4.2 KdV Denklemi İçin Backlund Dönüşümü 4.3 KdV Denklemi İçin Bilineer Formdaki Backlund Dönüşümü 4.4 Bilineer Formdaki Süperpozisyon Formülü 4.5 KdV Denkleminin N-Soliton Çözümleri 5 Boussinesq Denklemi 5.1 Boussinesq Denklemi İçin Bilineer Formdaki Backlund Dönüşümü 5.2 Boussinesq Denklemi İçin Bazı Çözümler 6 Sine-Gordon Denklemi 42 6.1 Sine-Gordon Denklemi İçin Backlund Dönüşümü 6.2 Sine-Gordon Denklemi İçin Bilineer Formdaki Backlund Dönüşümü 7 Ozdeşliklertr_TR
dc.language.isoturtr_TR
dc.publisherFen Bilimleri Enstitüsütr_TR
dc.rightsinfo:eu-repo/semantics/openAccesstr_TR
dc.subjectbacklund dönüşümü
dc.subjectpermüte edilebilirlik şartı
dc.subjecthirota metodu
dc.subjectsolitonlar
dc.subjectkorteweg-de vries denklemi
dc.subjectsine-gordon denklemi
dc.subjectboussinesq denklemi
dc.titleLineer Olmayan Kısmi Diferansiyel Denklemlerin Backlund Dönüşümleritr_TR
dc.typeinfo:eu-repo/semantics/masterThesistr_TR
dc.description.ozetBu tezde lineer olmayan denklemlerin Backlund dönüşümlerinin nasıl elde edildiği, bu dönüşümlerin kullanılması ile denklemlerin permüte edilebilirlik şartı kullanılarak elde edilen süperpozisyon formülleriyle, denklemlerin bilinen çözümlerinden yeni çözümlerin elde edilebileceği üzerine çalışılmıştır. Özel olarak matematiksel fizikte önemli yere sahip bazı denklemlerin 1-soliton çözümlerinden N-soliton çözümlerine ulaşılabileceğini göstererek, Backlund dönüşümlerinin integre edilebilirlik konusundaki yeri vurgulanmıştır. Bu amaçla Backlund dönüşümlerinin elde edilmesinde de kullanılan Hirota D-operatörü ve Hirota yöntemi anlatılmıştır. Bu bağlamda Korteweg-de Vries (KdV), Sine-Gordon (SG) ve Boussinesq denklemleri detaylı olarak incelenmiştir.tr_TR
dc.contributor.departmentMatematiktr_TR


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