Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Aslan, İsmailSubject: search.filters.subject.Burgers equation

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 9
    Citation - Scopus: 9
    Multi-Wave and Rational Solutions for Nonlinear Evolution Equations
    (Walter de Gruyter GmbH, 2010) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    Nonlinear evolution equations always admit multi-soliton and rational solutions. The Burgers equation is used as an example, and the exp-function method is used to eluciadte the solution procedure.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 8
    Similarity Solutions To Burgers' Equation in Terms of Special Functions of Mathematical Physics
    (Jagellonian University, 2017) Öziş, Turgut; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In this paper, the Lie group method is used to investigate some closed form solutions of famous Burgers' equation. A detailed and complete symmetry analysis is performed. By similarity transformations, the equation is reduced to ordinary differential equations whose general solutions are written in terms of the error function, Kummer's confluent hypergeometric function Φ(a; b; x) and Bessel functions Jp, showing the strong connection between the best mathematical modelling equations and the special functions of mathematical physics.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 15
    Constructing Rational and Multi-Wave Solutions To Higher Order Nees Via the Exp-Function Method
    (John Wiley and Sons Inc., 2011) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In this paper, we present an application of some known generalizations of the Exp-function method to the fifth-order Burgers and to the seventh-order Korteweg de Vries equations for the first time. The two examples show that the Exp-function method can be an effective alternative tool for explicitly constructing rational and multi-wave solutions with arbitrary parameters to higher order nonlinear evolution equations. Being straightforward and concise, as pointed out previously, this procedure does not require the bilinear representation of the equation considered.