Soyoğlu, Duygu

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https://hdl.handle.net/20.500.14365/7570
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Soyoglu, Duygu
Soyoglu, D.
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02.02. Mathematics
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Former Staff
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Scholarly Output

3

Articles

2

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Supervised PhD Theses

1

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1

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1

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Scopus Citations per Publication

0.33

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2

Supervised Theses

1

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Electronıc Journal of Dıfferentıal Equatıons1
Hacettepe Journal of Mathematıcs And Statıstıcs1
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2015 - 20173
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Now showing 1 - 3 of 3
  • Thumbnail Image
    Article
    Weak Solutions of a Hyperbolic-Type Partial Dynamic Equation in Banach Spaces
    (Hacettepe Univ, Fac Sci, 2015) Yantir, Ahmet; Soyoğlu, Duygu
    In this article, we prove an existence theorem regarding the weak solutions to the hyperbolic-type partial dynamic equation z(Gamma Delta)(x, y) = f(x, y, z(x, y)), x(x, 0) = 0, z(0, y) = 0 , x is an element of T-1, y is an element of T-2 in Banach spaces. For this purpose, by generalizing the definitions and results of Cichon et. al. we develop weak partial derivatives, double integrability and the mean value results for double integrals on time scales. DeBlasi measure of weak noncompactness and Kubiaczyk's fixed point theorem for the weakly sequentially continuous mappings are the essential tools to prove the main result.
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    Doctoral Thesis
    Unification of Integrable Q-Difference Equations [doctoral Thesis]
    (İzmir Ekonomi Üniversitesi, 2017) Soyoğlu, Duygu; Yantır, Burcu Silindir; Yıldız, Aslı
    Bu tezdeki amacımız integre edilebilen q-fark denklemlerini birleştirici tek bir denklem elde etmektir. Bu genelleştirilmiş q-Hirota-Miwa adındaki denklem, Hirota bilineer formdadır. Bu denklemin integrallenebilirliğini araştırdıktan sonra Hirota methodu ile üç-q-soliton çözümlerini bulduk. Bu denklem çeşitli q-fark denklemlerinin, Toda, KdV ve sine-Gordon gibi denklemlerin Hirota bilineer formlarını içermektedir. Çalışmadaki en önemli nokta, bu bilineer formları oluşturmak için uygun kısıtların Hirota-Miwa denkleminden elde edilmesi ve bu lineer formların sürekli Hirota bilineer formlara indirgenmesidir. Bu tezde, q-Hirota-Miwa denkleminden elde edilen q-Hirota bilineer formlar sonucunda, q-Toda, q-KdV ve q-sine Gordon denklemlerinin standart formlarının yanı sıra üç-q-soliton çözümlerini de inşa ettik.
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    Article
    Citation - Scopus: 1
    Unification of Integrable Q-Difference Equations
    (Texas State Univ, 2015) Silindir, Burcu; Soyoglu, Duygu
    This article presents a unifying framework for q-discrete equations. We introduce a generalized q-difference equation in Hirota bilinear form and develop the associated three-q-soliton solutions which are described in polynomials of power functions by utilizing Hirota direct method. Furthermore, we present that the generalized q-difference soliton equation reduces to q-analogues of Toda, KdV and sine-Gordon equations equipped with their three-q-soliton solutions by appropriate transformations.