Yazar "Ahmed, Muhammad Ozair" seçeneğine göre listele

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    Öğe
    Explicit solitary wave structures for the fractional-order Sobolev-type equations and their stability analysis
    (Elsevier, 2024) Shahzad, Tahir; Ahmed, Muhammad Ozair; Baber, Muhammad Zafarullah; Ahmed, Nauman; Akgul, Ali; Abdeljawad, Thabet; Amacha, Inas
    The current research is concerned with solitary wave structures to the time fractional -order Sobolev-type equations. The special types of Sobolev-type equations are under consideration such as the generalized hyperelastic-rod wave (HRW) equation, and Camassa-Holm (CH) equation. These equations occur in several fields, including particularly in quantum field theory, plasma theory, ecology, consolidation of clay and fluid dynamics. The underlying models are investigated analytically by applying two techniques, such as the generalized projective Riccati equation (GPRE) and the modified auxiliary equation (MAE). The gained results are obtained from the different families of solutions such as, including a periodic wave, kink -type wave peakon, a singular wave, and dark solutions. The gained results are denoted as hyperbolic and trigonometric functions. Furthermore, we check that the underlying models are stable using the concept of linearized stability. The propagation behavior of the gained results is displayed in 3D, 2D, and contour visualizations to investigate the influence of various relevant parameters. These results will help the researchers to understand the physical situations.
  • [ X ]
    Öğe
    Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis
    (Nature Portfolio, 2023) Shahzad, Tahir; Ahmed, Muhammad Ozair; Baber, Muhammad Zafarullah; Ahmed, Nauman; Akguel, Ali; El Din, Sayed M.
    In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel techniques used to explore the solitary wave structures namely as; generalized Riccati equation mapping and modified auxiliary equation (MAE) methods. The different types of abundant families of solutions in the form of dark soliton, bright soliton, solitary wave solutions, mixed singular soliton, mixed dark-bright soliton, periodic wave, and mixed periodic solutions. The linearized stability of the model has been investigated. Solitons behave differently in different circumstances, and their behaviour can be better understood by building unique physical problems with particular boundary conditions (BCs) and starting conditions (ICs) based on accurate soliton solutions. So, the choice of unique physical problems from various solutions is also carried out. The 3D, line graphs and corresponding contours are drawn with the help of the Mathematica software that explains the physical behavior of the state variable. This information can help the researchers in their understanding of the physical conditions.