A variety of multiple-soliton solutions for the integrable (4+1)-dimensional Fokas equation

In this work, we study the integrable nonlinear (4+1)-dimensional Fokas equation. By means of systematic use of the simplified Hirota's method, we demonstrate the generation of a variety of multiple-soliton solutions, and also multiple-complex soliton solutions, for this equation. We show that the set of multiple-soliton solutions is not unique, and each set is characterized by distinct dispersion relation, distinct transformation, and hence distinct physical structure. We confirm the integrability of this equation by showing it possesses the Painlev'e integrability in the sense of WTC method. Besides, some other solitonic, singular, and periodic solutions are given by using hyperbolic and trigonometric ansatze.