On the solutions and conservation laws of the (1+1)-dimensional higher-order Broer-Kaup system

In this paper we obtain exact solutions of the ( 1 + 1)-dimensional higher-order Broer-Kaup system which was obtained from the Kadomtsev-Petviashvili equation by the symmetry constraints. The methods used to determine the exact solutions of the underlying system are the Lie group analysis and the simplest equation method. The solutions obtained are the solitary wave solutions. Moreover, we derive the conservation laws of the (1 + 1)-dimensional higher-order Broer-Kaup system by employing the multiplier approach and the new conservation theorem.