Muhammad JawazMuhammad ShahzadNauman AhmedMuhammad Zafarullah BaberMuhammad IqbalAli Akgül2025-04-142025-04-142025-06Jawaz, M., Shahzad, M., Ahmed, N., Baber, M. Z., Iqbal, M., & Akgül, A. (2025). Analytical dynamics to the interactions of a diffusive mussel-algae model. Partial Differential Equations in Applied Mathematics, 101151.2666-8181https://doi.org/10.1016/j.padiff.2025.101151https://hdl.handle.net/20.500.12604/8585This 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 dynamicsinfo:eu-repo/semantics/closedAccessAlgebraicDynamicsPhenomenaPhysicalSystemTransformationsVelocityWave structuresjournal-article14Q12-s2.0-8600079797010.1016/j.padiff.2025.101151