Solitary waves and conservation laws of Bona-Chen equations

This paper obtains the solitary wave solution of the Bona-Chen equation which is a coupled system of nonlinear evolution equation that arises in the study of shallow water waves flow. The ansatz method and Jacobi elliptic function method are used to obtain the solutions. The conservation law of the equation is obtained by the multiplier method. Finally, the numerical simulations are also given.