Mathematics / Matematik

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

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Subject: search.filters.subject.Exact solutionsWoS Q: search.filters.wosQuartile.Q2

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Now showing 1 - 3 of 3
  • 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: 25
    Citation - Scopus: 27
    Some Remarks on Exp-Function Method and Its Applications
    (IOP Publishing Ltd., 2011) Aslan, İsmail; Marinakis, Vangelis
    Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.
  • Article
    Citation - WoS: 25
    Citation - Scopus: 25
    Exact and Explicit Solutions To the Discrete Nonlinear Schrödinger Equation With a Saturable Nonlinearity
    (Elsevier Ltd., 2011) Aslan, İsmail
    We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G′/G)-expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are constructed; hyperbolic, trigonometric, and rational which have not been explicitly computed before. © 2011 Elsevier B.V. All rights reserved.