Novel hybrid solitary waves and shrunken-periodic solutions, solitary Moiré pattern and conserved vectors of the (4+1)-Fokas equation.

In this paper, we present a comprehensive study on the (4 + 1) -Fokas equation that includes new solutions and conservation laws of the equation. Specifically, for the first time, new shrunken-periodic and fascinating interactions on the bright soliton background have been investigated. Furthermore, a bright, dark, dipole soliton, tripole soliton, multipole soliton, periodic, doubly-periodic, damped-periodic, kink, lump, rogue wave, breather and their interactions have been attained and graphically illustrated. In addition, a significant interaction between four parabolic-periodic solitary waves is first detected and emphasized by harnessing 3D and contour plots. On the other hand, the latter has been compared to an experimentally-induced Moiré effect from a monitor screen camera capture. These outstanding results are achieved using the Lie symmetry approach. The multiple reduction process of the (4 + 1) -Fokas equation through the Lie algebra spanned elements, and the corresponding optimal system guarantees 23 solutions in general forms. To determine the physical meaning of the latter, an appropriate ansatz for the arbitrary functions and parameters has been proposed and listed in the corresponding tables, which leads to the various types of solitary wave solutions. Finally, the conserved vectors for the underlying equation are derived using the multiplier method. [ABSTRACT FROM AUTHOR]