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In this piece of research, our aim is to investigate the novel solitons solutions of nonlinear (4+1)-dimensional Fokas equation (FE) and (2+1)-dimensional Breaking soliton equation (BSE) via new extended direct algebraic method. New acquired solutions are bright, singular, dark, periodic singular, combined dark-bright and combined dark-singular solitons along with hyperbolic and trigonometric functions solutions. We achieved different kinds of solitons solutions contain key applications in engineering and physics. By taking the appropriate values of these parameters, numerous novel structures are also plotted. These solutions define the wave performance of the governing models, actually. Furthermore, the physical understanding of the acquired solutions is revealed in forms of 3-D, 2-D and contour graphs for different appropriate parameters. From results, we conclude that the applied computational method is straight, talented and can be applied in more complex phenomena for such models.

Novel solitons solutions of two different nonlinear PDEs appear in engineering and physics