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

Exploring new wave soliton solutions to nonlinear partial differential equations has always been one of the most challenging issues in different 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 first-order rogue wave solution is also presented. We discuss the influence 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 first-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.

Automated summary

In this paper, multiple rogue wave solutions of the (3+1)-dimensional KdV-BBM equation are constructed using symbolic calculation methods. The localization features of first-order rogue wave solutions are analyzed, along with the influence of parameters on rogue wave characteristics. Polynomial functions are utilized to construct generalized multiple rogue waves with controllable centers, generating 3-rogue wave solutions, 6-rogue wave solutions, and 9-rogue wave solutions.