Numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order

In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, u_tt + au_xx + bu + cu^p + du^2p-1 = 0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions: numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions.