Analytic rogue wave solutions for a generalized fourth-order Boussinesq equation in fluid mechanics

Abstract

A bilinear transformation method is proposed to find the rogue wave solutions for a generalized fourth-order Boussinesq equation, which describes the wave motion in fluid mechanics. The one- and two-order rogue wave solutions are explicitly constructed via choosing polynomial functions in the bilinear form of the equation. The existence conditions for these solutions are also derived. Furthermore, the system parameter controls on the rogue waves are discussed. The three parameters involved in the equation can strongly impact the wave shapes, amplitudes, and distances between the wave peaks. The results can be used to deeply understand the nonlinear dynamical behaviors of the rogue waves in fluid mechanics.