New Bilinear Bäcklund Transformation and Higher Order Rogue Waves with Controllable Center of a Generalized (3+1)-Dimensional Nonlinear Wave Equation

In this paper, we first obtain a bilinear form with small perturbation u₀ for a generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles. Based on that, a new bilinear Bäcklund transformation which consists of four bilinear equations and involves seven arbitrary parameters is constructed. After that, by applying a new symbolic computation method, we construct the higher order rogue waves with controllable center to the generalized (3+1)-dimensional nonlinear wave equation. The rogue waves present new structure, which contain two free parameters α and β. The dynamic properties of the higher order rogue waves are demonstrated graphically. The graphs tell that the parameters α and β can control the center of the rogue waves.