New soliton wave structures of nonlinear (4 + 1)-dimensional Fokas dynamical model by using different methods

The physics of the (4 + 1)-dimensional Fokas equation follows necessarily from the physical nature of the Kadomtsev–Petviashvili and Davey-Stewartson equations in wave theory. In this article, we consider the nonlinear (4+1)-dimensional Fokas partial differential equation. Two recognizable methods namely improved F-expansion and generalized exp(-ϕ(ξ))-expansion methods are proposed to investigate the new wave structures of (4 + 1)-dimensional Fokas dynamical model which have never been constructed before. As a result, new solutions are in different solitons such as dark soliton, bright soliton, combined dark-bright soliton solutions, periodic, and solitary wave solutions. The new generalized solitary wave solutions can be constructed by assigning the specific values to those parameters involved in these methods. The achieved results are compared with existing results in the literature and we found that some of results are not available in literature. The derived results are explained graphically, to understand the phenomena of the proposed model. The constructed results rendering that the consider methods in this article are simple, effective, and easy to find the solution of many other nonlinear higher-dimensional models which arise in several areas of science and engineering.