The (1+1)-dimensional Mikhailov-Novikov-Wang (MNW) equation is studied dynamically using the unified technique
in this contribution. Solitons of various forms, such as those for trigonometric, periodic, exponential, elliptic, and other
functions, are obtained using this method. Through the use of an efficient unified technique, this work's findings
improve our comprehension of the equation's physical meaning and behaviour, illuminating the importance of studying
various nonlinear wave phenomena in ocean engineering and physics. None of the other writers have ever used these
derived findings in any of their prior studies. We use Mathematica to create 3-dimensional, contour, and 2-dimensional
plots that show the answers in graphical form for the sake of presentation and physical examples. As a result, we find
that several forms of soliton solutions, periodic solutions, anti-bell-shape solutions, kink wave solutions, solitary wave
solutions, and multisoliton solutions are gained for the MNW equations.