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.
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    Spatio-temporal patterns and Turing–Hopf bifurcation in a spatially extended prey–predator model with ratio-dependent interactions
    (Springer Science and Business Media LLC, 2025-04-16) Muhammad Waqas Yasin; Nauman Ahmed; Ali Akgül; Muhammad Zafarullah Baber; Dumitru Baleanu; Ovidiu Tintareanu-Mircea
    In this manuscript, we investigate the (2+1)-dimensional ratio-dependent prey–predator system. Prey–predator dynamics are a vital component of the eco-system. It provides the basic food for the living organisms. So, we considered the extended prey–predator model. The underlying model has 2 equilibrium points and stability analysis is carried out about the coexistence equilibrium. The condition for the Hopf bifurcation and Turing instabilities are derived. These conditions help to analyze the formation of patterns in the prey–predator system. The dispersion relation shows the changing behavior of Hopf bifurcation and Turing instability from stable to unstable. The bifurcation and Turing instability simulation divide the parametric space into 4 Regions. In Region I, the solution is stable, in Region II there is purely Turing instability, in Region III, there is only Hopf instability and in Region IV there is Hopf as well as Turing instability. Different types of Turing patterns are produced to capture rate parameters. The numerical solution of the model is obtained by positivity preserving finite difference scheme. The applied scheme is von Neumann stable, and consistent with the model. The bounded behavior of a given scheme is established. Mainly, we are focused on the graphical simulations for pattern formation and steady-state analysis. The 3D and 2D visualization for the Turing pattern and numerical solution are drawn for the various parameter values. The numerical simulations endorsed the analytical results.