On the solutions of the (1+1) and (2+1)-dimensional higher-order Broer-Kaup systems

In this work we study the (1+1) and (2+1)-dimensional higher-order Broer-Kaup (HBK) systems. The HBK systems were obtained from the inner parameter dependent symmetry constraints of the Kadomtsev-Petviashvili (KP) equation. The B?cklund transformations are used for a reliable treatment of these systems. We obtain multiple soliton solutions for the underlying systems. Moreover, we use a variety of hyperbolic functions methods and trigonometric methods to determine a variety of travelling wave solutions and periodic solutions.