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.

Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation

“…x and D 4 y . A soliton molecule and an asymmetric soliton can be constructed by selecting appropriate parameters in (8) or (9). These phenomena are shown in Figures 1 and 2.…”

“…The modified exponential expansion method is applied to the coupled Boussinesq equation [7]. The multisoliton solutions, breather solutions, and rogue waves of the generalized Boussinesq equation are obtained via the symbolic computation method [8] and the polynomial functions in the bilinear form [9]. Generally, seeking exact solutions to nonlinear evolution equations is a vital task in soliton theory.…”

Solitary and periodic wave solutions of the generalized fourth‐order Boussinesq equation via He's variational methods

“…Nonlinear partial differential equations are widely used to model different physical phenomena, 1–7 and its solution method is always the focus of research 8–15 . In this paper, we aim to study a fourth‐order nonlinear generalized Boussinesq water wave equation, which is given as follows 8,16 : where m , n , and k are arbitrary constants. η ( x , t ) is a physical quantity that represents the energy field in fluid mechanics, t and x represent time and displacement, respectively.…”

Controllable symmetry breaking solutions for a nonlocal Boussinesq system

“…The bilinear transformation method was proposed to find the rogue wave solutions for the above generalized Eq. (1) 21 . Two exponential-type integrators were proposed and analyzed for the “good” Boussinesq equation, i.e.…”