Degenerate lump chain solutions of (4+1)-dimensional Fokas equation

This paper takes (4+1)-dimensional Fokas equation as an example to introduce an ingenious limit approach to generate degenerate solutions in detail. Under this technique, we start with solutions describing lump chains and obtain degenerate solutions from coupled lump chains quickly and easily. The complex dynamics of these degenerate solutions are shown in both three-dimensional plots and two-dimensional contour plots. Additionally, we find the central area of the degenerate solutions is a very good approximation of corresponding rogue wave solutions which can be used to formulate the rogue waves in a optical system. •An ingenious limit approach is introduced to generate some degenerate solutions for PDEs.•Degenerate solutions of (4+1)-dimensional Fokas equation are derived by the method from coupled lump chains.•The complex dynamics of these degenerate solutions are discussed in detail and shown by some plots.•The central area of degenerate solutions is a very good approximation of corresponding rogue wave solutions.