Oluşum tipi lineer olmayan parça türevli diferensiyel denklemlerin tam çözümleri
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Date
2019-05-06
Authors
Yıldırım, Yakup
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Publisher
Bursa Uludağ Üniversitesi
Abstract
Bu tez çalışmasında oluşum tipi lineer olmayan parça türevli diferensiyel denklemlerin tam çözümleri araştırılmıştır. (1+1) boyutlu genelleştirilmiş bir Korteweg–de Vries denklemi, (2+1) boyutlu Sawada–Kotera denklemi, yeni genelleştirilmiş bir (3+1) boyutlu lineer olmayan oluşum türü denklemi, (2+1) boyutlu yerel olmayan Ito denklemi, (2+1) boyutlu kırılgan soliton denklemi ve yedinci mertebeden kesirli Sawada–Kotera–Ito denklemlerinin tam çözümleri elde edilmiştir. İlerleyen dalga çözümü, knoidal dalga çözümü, sinoidal dalga çözümü, bir soliton çözümü, iki soliton çözümü, üç soliton çözümü, kompleksiton çözümü, çoklu soliton çözümü, lump tipi çözümü, rasyonel çözümü, soliton çözümü, poziton çözümü, negaton çözümü, rasyonel-soliton-poziton etkileşim çözümü ve kuvvet seri çözümleri elde edilmiştir. Bu çözümlerin elde edilmesi için en basit denklem metodu, yeni test fonksiyon metodu, çoklu eksponansiyel fonksiyon metodu, geliştirilmiş rasyonel fonksiyon metodu, lump ve lump tipi çözüm algoritması, Wronskian determinant algoritması, kuvvet seri metodu ve Lie simetri yaklaşımları tüm adımlarıyla birlikte sunulmuştur.
In this thesis study, the exact solutions to evolution type nonlinear partial differential equations have been investigated. The exact solutions to (1+1)-dimensional an extended Korteweg–de Vries equation, (2+1)-dimensional Sawada-Kotera equation, a new extended (3+1)-dimensional nonlinear evolution equation, (2+1)-dimensional non-local Ito equation, (2+1)- dimensional the breaking soliton equation and seventh-order time fractional Sawada-Kotera-Ito equation have been obtained. The traveling wave solution, cnoidal wave solution, snoidal wave solution, one soliton solution, two soliton solution, three soliton solution, complexiton solution, multi-soliton solution, lump-type solution, rational solution, soliton solution, positon solution, negaton solution, rational-soliton-positon interaction solution and power series solutions have been obtained. In order to obtain these solutions, the simplest equation method, novel test function method, multiple exp-function method, extended transformed rational function method, lump and lump-type solution algorithm, Wronskian determinant algorithm, power series method and Lie symmetry approaches together with all the steps have been presented.
In this thesis study, the exact solutions to evolution type nonlinear partial differential equations have been investigated. The exact solutions to (1+1)-dimensional an extended Korteweg–de Vries equation, (2+1)-dimensional Sawada-Kotera equation, a new extended (3+1)-dimensional nonlinear evolution equation, (2+1)-dimensional non-local Ito equation, (2+1)- dimensional the breaking soliton equation and seventh-order time fractional Sawada-Kotera-Ito equation have been obtained. The traveling wave solution, cnoidal wave solution, snoidal wave solution, one soliton solution, two soliton solution, three soliton solution, complexiton solution, multi-soliton solution, lump-type solution, rational solution, soliton solution, positon solution, negaton solution, rational-soliton-positon interaction solution and power series solutions have been obtained. In order to obtain these solutions, the simplest equation method, novel test function method, multiple exp-function method, extended transformed rational function method, lump and lump-type solution algorithm, Wronskian determinant algorithm, power series method and Lie symmetry approaches together with all the steps have been presented.
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Keywords
Hirota türev operatörleri, Lie simetrileri, Genelleştirilmiş Hirota türev operatörleri, Wronskian determinantı, Riemann–Liouville kesir türevi, Tam çözümler, Hirota derivative operators, Lie symmet ries, Generalized Hirota derivative operators, Wronskian determinant, Riemann–Liouville fractional derivative, Exact solutions
Citation
Yıldırım, Y. (2019). Oluşum tipi lineer olmayan parça türevli diferensiyel denklemlerin tam çözümleri. Yayınlanmamış doktora tezi. Bursa Uludağ Üniversitesi Fen Bilimleri Enstitüsü.