Propagation of lump and traveling wave solutions to the $(4+1)$-dimensional Fokas equation arising in mathematical physics

In this paper, the $(4+1)$-dimensional Fokas model is investigated analytically with extensive applications in nonlinear wave theory including the evolution of a three-dimensional wave packet in water with a finite depth, and surface waves and internal waves in straits or channels of varied depth and width. Applying the Hirota bilinear approach, the lump wave solitons and interaction of lump with periodic waves, the interactions of lump wave along single, double-kink solitons as well as the interactions of lump, periodic along double-kink solitons of the governing model are developed. Additionally, by using the extended tanh function technique, certain new traveling wave solitons are established. The physical nature of several solitons is illustrated by drawing the 3D, contours and 2D plots. Consequently, a set of periodic, bright, dark, rational as well as elliptic function solitons are constructed. The employed techniques seem to be more effective and well organized to build some interesting analytical wave solitons to several appealing nonlinear models.