Multistage optimal homotopy asymptotic method for the K(2,2) equation arising in solitary waves theory

The paper is concern to the approximate analytical solution of K(2,2) using the multistage homotopy asymptotic method which are used in modern physics and engineering. The suggested algorithm is an accurate, effective, and simple to-utilize semi-analytic tool for non-linear problems, and in this manner the current investigation highlights the efficiency and accuracy of the method for the solution of non-linear PDE for large time span. Numerical comparison with the variational iteration method and with homotopy asymptotic method shows the efficacy and accuracy of the proposed method.