Yazar "Hussain, Shabbir" seçeneğine göre listele

Listeleniyor 1 - 2 / 2
  • [ X ]
    Öğe
    Analyzing multiplicative noise effects on stochastic dynamical ?4 equation using the new extended direct algebraic method
    (Elsevier, 2024) Manzoor, Zuha; Iqbal, Muhammad Sajid; Omer, Nader; Zakarya, Mohammed; Kanan, Mohammad; Akgul, Ali; Hussain, Shabbir
    The stochastic dynamical phi(4) equation is obtained by adding a multiplicative noise term to the classical phi(4) equation. The noise term represents the random fluctuations that are present in the system and is modeled by a Wiener process. The stochastic dynamical phi(4) equation is a powerful tool for modeling the behavior of complex systems that exhibit randomness and nonlinearity. It has a wide range of applications in physics, chemistry, biology, and finance. Our goal of this paper is to use the new extended direct algebraic method to find the stochastic traveling wave solutions of the dynamical phi(4) equation. We explore the new trigonometric, hyperbolic, and rational functions using the new extended direct algebraic method. Furthermore, we use Matlab to plot 3D surfaces of exact solutions to show how multiplicative noise affects the solutions to the stochastic dynamical phi(4) equation.
  • [ X ]
    Öğe
    The extended Fan's sub-equation method and its application to nonlinear Schrodinger equation with saturable nonlinearity
    (Elsevier, 2023) Ashraf, Romana; Hussain, Shabbir; Ashraf, Farrah; Akgul, Ali; El Din, Sayed M.
    This article discusses the saturable nonlinear Schrodinger equation, which is a key equation in the study of condensed matter physics, plasma physics, and nonlinear optics. This equation, which represents how electromagnetic waves behave in nonlinear media, is distinct because of its nonlinearity and dispersive properties. In this article, the extended Fan's sub equation method is used to construct novel solitary wave solutions of the saturable nonlinear Schrodinger equation. This method is a powerful tool for dealing with nonlinear partial differential equations and has been used to a wide range of problems in several branches of mathematics. According to the this method, the saturable nonlinear Schrodinger equation admits a wide range of exact solution families that rely on five parameters. These solutions include soliton-like solutions, which are localized waves that maintain their shape and speed over long distances, and triangular-type solutions, which have a triangular shape. The study also identifies single and combined non-degenerate Jacobi elliptic function like solutions. These solutions are a particular class of periodic function that appears in several branches of physics, including electromagnetism, quantum mechanics, and fluid dynamics. The obtained solutions are graphically represented by 3D, contour, and 2D graphs using MATLAB. The results of this article present novel perspectives on the saturable nonlinear Schrodinger equation and its possible applications in a different fields. These findings have important implications for nonlinear optics, the development of new optical devices, nonlinear optics, and related fields.