On quasi-periodic waves and rogue waves to the (4+1)-dimensional nonlinear Fokas equation

Abstract

Under investigation in this paper is the (4+1)-dimensional nonlinear Fokas equation, which is an important physics model. With the aid of Bell’s polynomials, an effective and straightforward method is presented to succinctly construct the bilinear representation of the equation. By using the resulting bilinear formalism, the soliton solutions and Riemann theta function periodic wave solutions of the equation are well constructed. Furthermore, the extended homoclinic test method is employed to construct the breather wave solutions and rogue wave solutions of the equation. Finally, a connection between periodic wave solutions and soliton solutions is systematically established. The results show that the periodic waves tend to solitary waves under a limiting procedure.