Mathematics / Matematik

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

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Publisher: search.filters.publisher.Elsevier Ltd.Subject: search.filters.subject.Exact solutions

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 23
    Citation - Scopus: 24
    Exact Solutions of Forced Burgers Equations With Time Variable Coefficients
    (Elsevier Ltd., 2013) Atılgan Büyükaşık, Şirin; Pashaev, Oktay
    In this paper, we consider a forced Burgers equation with time variable coefficients of the form Ut+(μ̇(t)/μ(t))U+UUx=(1/2μ(t))Uxx-ω2(t)x, and obtain an explicit solution of the general initial value problem in terms of a corresponding second order linear ordinary differential equation. Special exact solutions such as generalized shock and multi-shock waves, triangular wave, N-wave and rational type solutions are found and discussed. Then, we introduce forced Burgers equations with constant damping and an exponentially decaying diffusion coefficient as exactly solvable models. Different type of exact solutions are obtained for the critical, over and under damping cases, and their behavior is illustrated explicitly. In particular, the existence of inelastic type of collisions is observed by constructing multi-shock wave solutions, and for the rational type solutions the motion of the pole singularities is described.
  • 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.
  • Article
    Citation - WoS: 77
    Citation - Scopus: 110
    Analytic Study on Two Nonlinear Evolution Equations by Using the (g'/g)-expansion Method
    (Elsevier Ltd., 2009) Aslan, İsmail; Öziş, Turgut
    The validity and reliability of the so-called (G′/G)-expansion method is tested by applying it to two nonlinear evolutionary equations. Solutions in more general forms are obtained. When the parameters are taken as special values, it is observed that the previously known solutions can be recovered. New rational function solutions are also presented. Being concise and less restrictive, the method can be applied to many nonlinear partial differential equations.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 10
    Comment On: "new Exact Solutions for the Kawahara Equation Using Exp-Function Method" [j. Comput. Appl. Math. 233 (2009) 97102]
    (Elsevier Ltd., 2010) Aslan, İsmail
    Assas [Laila M.B. Assas, New exact solutions for the Kawahara equation using Exp-function method, J. Comput. Appl. Math. 233 (2009) 97102] found some supposedly new exact solutions to the Kawahara equation by means of the Exp-function method. Unfortunately, they are incorrect. We emphasize that the article contains erroneous formulas and resulting relations. In fact, no numerical method was used. © 2010 Elsevier B.V. All rights reserved.