Parameter limit method and its application in the (4+1)-dimensional Fokas equation

A new Hirota's bilinear form of the (4+1)-dimensional Fokas equation is obtained by an appropriate wave transformation. Applying the parameter limit method introduced in this paper, we obtain two homoclinic solutions and a rogue wave solution of (4+1)-dimensional Fokas equation. Besides, we also discuss the interaction between rogue wave solution and different forms of stripe solitons (one stripe soliton and double stripe solitons), and investigate the annihilation and emergence of rogue waves. Finally, the parametric reasons of soliton fusion and fission are discussed, furthermore, the fusion and fission phenomena of soliton are simulated by three-dimensional plots.