Spatio-temporal dynamics and interaction of lump solutions for the (4+1)-D Fokas equation

The (4+1)-D Fokas equation is a new and important physical model. Its Hirota's bilinear form with a perturbation parameter is obtained by an appropriate transformation. A class of lump solutions and three different forms of spatio-temporal structure are obtained. Meanwhile, the theoretical analysis for the change of spatio-temporal structure is discussed by using the extreme value theory of multivariate function. Finally, the interaction between a stripe soliton and lump solution is discussed, and a new wave phenomenon that the lump solution is swallowed and drowned by the stripe soliton is investigated.