Abstract
•Applications of mathematical physics models.•The hydrodynamic mathematical methods•Solitary waves solutions, periodic solutions, solitons.
Manuscript purpose is to find analytical solutions of the (2 + 1)-dimensional Heisenberg Ferromagnetic Spin Chain and Vakhnenko dynamical equations by using the generalized direct algebraic and simple equation analytical methods. Numerous exact traveling results are obtained in exponential, trigonometric and hyperbolic wave solutions. To understand the physical behavior of the models, the two and three dimensions graphs along with contour are plotted after assigning the particular values to the parameters. Obtained structures provide a rich platform for solving nonlinear wave problems with many applications.