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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