Exact solitary-wave solutions for the nonlinear dispersive K(2,2,1) and K(3,3,1) equations

We implemented homotopy analysis method for approximating the solution to the nonlinear dispersive K(m,p,1) type equations. By using this scheme, the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. To illustrate the application of this method, numerical results are derived by using the calculated components of the homotopy analysis series.