Investigation the soliton solutions of mussel and algae model leading to concentration

In this study, the abundant families of soliton solutions are constructed for the mussel -algae model which provides information about represents the concentration of algae in the water layer, and mussel biomass of sediment surface in the per square meter. These solutions are extracted in the form of shock singular, complex solitary-shock, shock-singular and periodic-singular. Also, the rational solutions are also emerged during the derivation. For these solutions we are used the new modified extended direct algebraic (NMEDA) technique. These solutions are gained by the help of Mathematica. Additionally, the physical behaviors of some solutions are shown for different values of parameters, the graphs in 3D-dimensions along with their contour diagrams are also drawn.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).