Higher-order rogue wave solutions of the Kadomtsev Petviashvili—Benjanim Bona Mahony (KP-BBM) model via the Hirota-bilinear approach. (16th October 2020) - Hoque, Md Fazlul; Roshid, Harun-Or-; Alshammari, Fahad Sameer
Abstract: We study the higher-order rogue wave solutions of the Kadomtsev Petviashvili—Benjanim Bona Mahony (KP-BBM) model with and without controllable center via the Hirota bilinear approach. To construct higher-order rogue wave solutions of the model, we apply cross-product terms in a polynomial expression as a test function. We construct three kinds of rogue waves with center at the origin and three kinds of higher-order rogue waves with a controllable center by choosing different test functions. We show how the center can control the shapes and orders of the rogue waves by choosing the values of parameters of the center. In particular, the 3-rogue wave solutions exhibit double rogue waves for lower values and distinct triple rogue waves in a triangular structure for a sufficiently large value parameters of the center. Moreover, the 6-rogue wave solutions of the model present lower-order rogue waves for small values and higher-order rogue waves for large value parameters of the center. It is shown that the order of the rogue gradually increases for rising value of parameters, and it will be maximum six distinct rogues for a sufficiently large values. Finally, we explain the solutions of the model in 3D and in density plots graphically.