Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Subject: search.filters.subject.Differential equationsWoS Q: search.filters.wosQuartile.Q2

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 11
    Citation - Scopus: 12
    Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types
    (IOP Publishing Ltd., 2016) Aslan, İsmail
    Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous. Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations, the majority of the results deal with polynomial types. Limited research has been reported regarding such equations of rational type. In this paper we present an adaptation of the (G′/G)-expansion method to solve nonlinear rational differential-difference equations. The procedure is demonstrated using two distinct equations. Our approach allows one to construct three types of exact traveling wave solutions (hyperbolic, trigonometric, and rational) by means of the simplified form of the auxiliary equation method with reduced parameters. Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.
  • Article
    Citation - WoS: 36
    Citation - Scopus: 40
    Exact Solutions for a Local Fractional Dde Associated With a Nonlinear Transmission Line
    (IOP Publishing Ltd., 2016) Aslan, İsmail
    Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions (kink/antikink solitons, singular, periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 15
    Exact Solutions of a Fractional-Type Differential-Difference Equation Related To Discrete Mkdv Equation
    (IOP Publishing Ltd., 2014) Aslan, İsmail
    The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before.
  • Article
    Citation - WoS: 26
    Citation - Scopus: 27
    Analytic Solutions To Nonlinear Differential-Difference Equations by Means of the Extended (g'/g)-expansion Method
    (IOP Publishing Ltd., 2010) Aslan, İsmail
    In this paper, a discrete extension of the (G′/G)-expansion method is applied to a relativistic Toda lattice system and a discrete nonlinear Schrödinger equation in order to obtain discrete traveling wave solutions. Closed form solutions with more arbitrary parameters, which reduce to solitary and periodic waves, are exhibited. New rational solutions are also obtained. The method is straightforward and concise, and its applications in physical sciences are promising. © 2010 IOP Publishing Ltd.