Yazar "Muhammad Zafarullah Baber" seçeneğine göre listele

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    Analytical dynamics to the interactions of a diffusive mussel–algae model
    (Elsevier BV, 2025-06) Muhammad Jawaz; Muhammad Shahzad; Nauman Ahmed; Muhammad Zafarullah Baber; Muhammad Iqbal; Ali Akgül
    This paper examines the diffusive mussel–algae model and explores soliton solutions and wave structures using advanced analytical techniques, particularly the new auxiliary equation method. The proposed method reveals a variety of solution types, including hyperbolic, parabolic, and mixed forms. These closed-form results provide the nature of the current problem. These solutions are validated against known results and numerical simulations. Additionally, we describe two-dimensional and three-dimensional graphical representations of the solutions, illustrating their spatial and temporal dynamics. This study enhances the theoretical understanding of mussel algae interactions and offers practical insights for eco-logical management, showcasing the contributions of the approach to resolving complex ecological dynamics
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    Reliable numerical scheme for coupled nonlinear Schrödinger equation under the influence of the multiplicative time noise
    (Springer Science and Business Media LLC, 2025-03-28) Muhammad Zafarullah Baber; Nauman Ahmed; Muhammad Waqas Yasin; Muhammad Sajid Iqbal; Ali Akgül; Murad Khan Hassani; Muhammad Jawaz
    In this study, we consider the coupled nonlinear Schrödinger equation under the influence of the multiplicative time noise. The coupled nonlinear Schrödinger equation, which shows the complex envelope amplitudes of the two modulated weakly resonant waves in two polarisations and is used to describe the pulse propagation in high birefringence fibre, has several uses in optical fibres.query:Journal instruction requires a city for affiliations; however, these are missing in affiliation [6]. Please verify if the provided city are correct and amend if necessary. The underlying model is analyzed numerically and analytically as well. For the computational results, the proposed stochastic backward Euler scheme is developed and its consistency is derived in the mean square sense. For the linear stability analysis, Von-Neumann criteria is used, given proposed stochastic scheme is unconditionally stable. The exact optical soliton solutions are constructed with the help of the [Formula: see text]-model expansion technique, which provided us with the Jacobi elliptic function solutions that will explore optical solitons and solitary waves as well. The initial and boundary conditions are constructed for the numerical result by some optical soliton solutions. The 3D, 2D and corresponding contour plot are drawn for the different values of noise. Mainly, the comparison of results is shown graphically in 3D and line plots for some newly constructed solutions by selecting suitable parameters value.