• Ana Sayfa

Unification of integrable q-difference equations

Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: İzmir Ekonomi Üniversitesi, Fen Bilimleri Enstitüsü, Türkiye

Tezin Onay Tarihi: 2017

Tezin Dili: İngilizce

Öğrenci: DUYGU SOYOĞLU

Danışman: Burcu Silindir Yantır

Özet:

In this thesis our aim is to detect an equation which is a unification of integrable q-difference equations. This generalized equation, namely q-Hirota-Miwa equation, is in Hirota bilinear form. We search the existence of its integrability and find three-q-soliton solutions by Hirota's method. This generalized equation includes bilinear forms of several q-difference equations, such as q-analogues of Toda, KdV and sine-Gordon equations. Not only one of the most important point is to meet with suitable reductions for constructing bilinear forms from Hirota-Miwa equation, but also the key point is that Hirota bilinear forms must also recover their continuous bilinear forms. In this thesis, as a result of q-deformed Hirota bilinear forms reduced from q-Hirota-Miwa equation, we construct standard form of q-Toda, q-KdV and q-sine-Gordon equations as well as their three-q-soltions solutions.