Lineer olmayan kısmi türevleri diferansiyel denklemlerin yarı-analitik çözümleri üzerine
Küçük Resim Yok
Tarih
2005
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Ege Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
V ÖZET LİNEER OLMAYAN KISMİ TÜREVLİ DİFERANSİYEL DENKLEMLERİN YARI-ANALİTİK ÇÖZÜMLERİ ÜZERİNE YILDIRIM, Ahmet Yüksek Lisans Tezi, Matematik Bölümü Tez Yöneticisi : Prof.Dr.Turgut ÖZİŞ Ekim 2005, 189 sayfa Şok dalgalan,su dalgalan,solitonlar ve solitary dalgalan ile ilgili olan dalga problemlerinin en iyi bilinen örneklerini tanıttık.İlk olarak lineer olmayan dağılım dalgalarım, Whitham Denklemini ve Whitham Ortalama Varyasyonel Prensibini tanımladık.Bunu Whitham Kararsızlık Analizi ve onun lineer olmayan su dalgalarına uygulaması izledi. Ayrıca fiziksel uygulamalarıyla beraber lineer olmayan Difuzyon- Reaksiyon Fenomenini,Burgers ve Fisher Denklemlerini verdik.Özellikle gezen dalga çözümlerini ve onların kararlılık analizini,benzerlik metotlarım ve difüzyon denMemlerinin benzerlik çözümlerini gösterdik. Son olarak Ters Saçılım Dönüşümü Teorisini anlattık.Korteweg-de Vries (KdV) ve Boussinesq Denldemlerinin temel özellikleri üzerine olan bazı son sonuçlar detaylı olarak tartışıldı.Ayrıca Backmnd Dönüşümleri,lineer olmayan süperpozisyon prensibi,Lax Formulasyonu ve onun KdV hiyerarşisi de içeriğe dahil edildi. Anahtar sözcüklenLineer olmayan dağılım dalgalan, Whitham Denklemi,Lineer olmayan Difüzyon-Reaksiyon Fenomeni,Burgers ve Fisher Denklemleri,Benzerlik metotlan ve benzerlik çözümleri,Ters Saçılım Dönüşümü,Korteweg-de Vries (KdV),Boussinesq Denklemleri,Backlund Dönüşümleri,Lax Formulasyonu,KdV hiyerarşisi
VII ABSTRACT ON SEMI-ANALYTICAL SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS YILDIRIM, Ahmet MSc Thesis, Mathematics Department Supervisor: Prof.Dr. Turgut ÖZİŞ October 2005, 189 pages We introduced the best known examples of wave problems are the corresponding shock waves,water waves,solitons and solitary waves.Firstly,we defined nonlinear dispersive waves,Whitham's Equations and Whitham's Averaged Variational Principle.This was followed by the Whitham Instability Analysis and its applications to nonlinear water waves. Also we gave the nonlinear Diffusion-Reaction Phenomena,Burgers' and Fisher's equations with physical applications. Specially we showed travelling wave solutions and their stability analysis,similarity methods and similarity solutions of diffusion equations. At last,we explained the theory of the Inverse Scattering Transform.Many recent results on the basic properties of the Korteweg-de Vries (KdV) and Boussinesq Equations were discussed in some detail.Included were Backhand Transformations,nonlinear superposition principle,the Lax Formulation and its KdV hiyerarchy. Key words: Nonlinear Dispersive Waves, Whitham's Equations, Nonlinear Diffusion-Reaction Phenomena, Burgers' and Fisher's equations, Similarity methods and similarity solutions, Inverse Scattering Transform, Korteweg- de Vries (KdV), Boussinesq Equations, Backhand Transformations, Lax Formulation, KdV hiyerarchy.
VII ABSTRACT ON SEMI-ANALYTICAL SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS YILDIRIM, Ahmet MSc Thesis, Mathematics Department Supervisor: Prof.Dr. Turgut ÖZİŞ October 2005, 189 pages We introduced the best known examples of wave problems are the corresponding shock waves,water waves,solitons and solitary waves.Firstly,we defined nonlinear dispersive waves,Whitham's Equations and Whitham's Averaged Variational Principle.This was followed by the Whitham Instability Analysis and its applications to nonlinear water waves. Also we gave the nonlinear Diffusion-Reaction Phenomena,Burgers' and Fisher's equations with physical applications. Specially we showed travelling wave solutions and their stability analysis,similarity methods and similarity solutions of diffusion equations. At last,we explained the theory of the Inverse Scattering Transform.Many recent results on the basic properties of the Korteweg-de Vries (KdV) and Boussinesq Equations were discussed in some detail.Included were Backhand Transformations,nonlinear superposition principle,the Lax Formulation and its KdV hiyerarchy. Key words: Nonlinear Dispersive Waves, Whitham's Equations, Nonlinear Diffusion-Reaction Phenomena, Burgers' and Fisher's equations, Similarity methods and similarity solutions, Inverse Scattering Transform, Korteweg- de Vries (KdV), Boussinesq Equations, Backhand Transformations, Lax Formulation, KdV hiyerarchy.
Açıklama
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Anahtar Kelimeler
Matematik, Mathematics