Yazar "Iskenderoglu, Gulistan" seçeneğine göre listele

Listeleniyor 1 - 4 / 4
  • Küçük Resim
    Öğe
    Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method
    (Elsevier, 2022) Iskenderoglu, Gulistan; Kaya, Dogan
    In this work, we present an application of Lie group analysis to study the generalized derivative nonlinear Schrodinger ¨ equation, which governs the evolution of a nonlinear wave and plays an important role in the propagation of short pulses in optical fiber systems. To construct Lie group reductions, we study the symmetry properties and introduce various infinitesimal operators. Further, we obtain self-similar solutions and periodic soliton solutions of the generalized derivative nonlinear Schrodinger ¨ equation. This type of solution plays a vital role in the study of the blow-up and asymptotic behavior of non-global solutions. And at the end, we present graphs for each solution by considering the physical meaning of the solutions.
  • Küçük Resim
    Öğe
    ON LIE GROUP ANALYSIS OF BOUNDARY VALUE PROBLEM WITH CAPUTO FRACTIONAL DERIVATIVE
    (YILDIZ TECHNICAL UNIV, 2019) Iskenderoglu, Gulistan; Kaya, Dogan
    Lie symmetry analysis of initial and boundary value problem for partial differential equations with Caputo fractional derivative is investigated. Also given generalized definition and theorem for symmetry method for partial differential equation with Caputo fractional derivative. The group symmetries and examples on reduction of fractional partial differential equations with initial and boundary conditions to nonlinear ordinary differential equations with initial condition are present.
  • Küçük Resim
    Öğe
    Symmetry Analysis and Conservation Laws of the Boundary Value Problems for Time-Fractional Generalized Burgers’ Differential Equation
    (2019) Iskenderoglu, Gulistan; Kaya, Doğan
    Many physical phenomena in nature can be described or modeled via a differential equation or a system of differential equations. In this work, we restrict our attention to research a solution of fractional nonlinear generalized Burgers’ differential equations. Thereby we find some exact solutions for the nonlinear generalized Burgers’ differential equation with a fractional derivative, which has domain as $\mathbb{R}^2$ ×$\mathbb{R}^+$. Here we use the Lie groups method. After applying the Lie groups to the boundary value problem we get the partial differential equations on the domain $\mathbb{R}^2$ with reduced boundary and initial conditions. Also, we find conservation laws for the nonlinear generalized Burgers’ differential equation.
  • Küçük Resim Yok
    Öğe
    Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense
    (PERGAMON-ELSEVIER SCIENCE LTD, 2020) Iskenderoglu, Gulistan; Kaya, Dogan
    In this work, we study Lie symmetry analysis of initial and boundary value problems (IBVPs) for partial differential equations (PDE) with Caputo fractional derivative. According to Bluman's definition and theorem for the symmetry analysis of the PDE system, we determine the symmetries of the PDE with Caputo fractional derivative in general form and prove theorem for the above equation. We investigate the symmetry analysis of IBVP for a fractional diffusion and third-order fractional partial differential equation (FPDE). And as a result of applying the method, we get several solutions. (C) 2020 Elsevier Ltd. All rights reserved.