Dark and kink soliton solutions of the generalized ZK-BBM equation by iterative scheme

The generalized ZK-BBM equation is solved using iterative scheme of the Adomian decomposition method (ADM) and variational iteration method (VIM). A dark and a kink soliton solutions of the generalized ZK-BBM equation are obtained under initial conditions. The convergence analysis of the ADM and VIM solution shows that these solutions are convergent. The comparison of the ADM and VIM solutions with the exact solution shows that the solutions of the generalized ZK-BBM equation by the iterative methods are almost exact. The absolute errors show that the accuracy and efficiency of the ADM and VIM depend on the problem and its domain. It is found that the iterative scheme of Adomian decomposition method and variational iteration method are quite efficient for the soliton solution of the generalized ZK-BBM equation.