Elastic and resonant interactions of a lump and two parallel line solitary waves for the (4+1)-dimensional Fokas equation

In this paper, by using of the Hirota bilinear method and the long wave limit method, we consider elastic interactions and resonant interactions of a lump and two parallel line solitary waves of the (4+1)-dimensional Fokas equation. We find that the phase shifts of the obtained lumps play an important role in the interactions and three different types of elastic interactions are obtained when the phase shifts are larger than zero. When the phase shifts tend to infinity, we find partially resonant interactions and completely resonant interactions of a lump and two parallel line solitary waves. The asymptotic interaction behaviors of the obtained solutions are analyzed in detail and illustrated graphically.