Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

Abstract

The purpose of this paper is to report the feasibility of constructing high-order rogue waves with controllable fission and asymmetry for high-dimensional nonlinear evolution equations. Such a nonlinear model considered in this paper as the concrete example is the (3+1)-dimensional generalized Boussinesq (gB) equation, and the corresponding method is Zhaqilao’s symbolic computation approach containing two embedded parameters. It is indicated by the (3+1)-dimensional gB equation that the embedded parameters can not only control the center of the first-order rogue wave, but also control the number of the wave peaks split from higher-order rogue waves and the asymmetry of higher-order rogue waves about the coordinate axes. The main novelty of this paper is that the obtained results and findings can provide useful supplements to the method used and the controllability of higher-order rogue waves.

Three-wave lump solutions and their dynamic behaviors for the (3+1)-dimensional constant-coefficient and variable-coeffcient differential equations

“…where , a b and γ are any non-zero constants [30]. It can be used to describe the motion of long waves in shallow water under the action of gravity in a nonlinear lattice [50].…”

“…For example, Gai et al obtained soliton solutions for the (3+1)-dimensional Boussinesq equation and analyzed the interactions of solitons [29]. Zhang et al studied higher-order rogue wave solutions for the (3+1)-dimensional generalized Boussinesq equation [30]. Since the variable-coefficient differential equations are more real and abundant than the corresponding constant-coefficient differential equations in describing physical phenomena and dynamics [31,32], so it has been widely concerned by scholars.…”