On constructing of multiple rogue wave solutions to the (3+1)-dimensional Korteweg–de Vries Benjamin-Bona-Mahony equation

Abstract

Exploring new wave soliton solutions to nonlinear partial dierential equations has always been one of the most challenging issues in dierent branches of science, including physics, applied mathematics and engineering. In this paper, we construct multiple rogue waves of (3+1)-dimensional Korteweg-de Vries Benjamin-Bona-Mahony equation through a symbolic calculation approach. Further, a detailed analysis of the localization features of rst-order rogue wave solution is also presented. We discuss the in uence of the parameters in the equation on the localization and characteristics of a rogue wave, as well as the control of their amplitude, depth, and width. In order to achieve these desired results, a series of polynomial functions are utilized to construct the generalized multiple rogue waves with a controllable center. Based on the bilinear form of this equation, 3-rogue wave solutions, 6-rogue wave solutions, and 9-rogue wave solutions are generated, respectively. The 3-rogue wave has a \triangle-shaped" structure. The center of the 6-rogue wave forms a circle around a single rogue wave. The 9-rogue wave consists of seven rst-order rogue waves and one second-order rogue waves as the center. Taking some appropriate parameters into account, their complex and interesting dynamics are shown in three-dimensional and contour plots. These new results are useful to understand the new features of nonlinear dynamics in real-world applications.