Exact solutions of some nonlinear partial differential equations using the variational iteration method linked with Laplace transforms and the Padé technique

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger’s equation, compacton k(n,n)k(n,n) equation, Zakharov–Kuznetsov Zk(n,n) equation, and KdV and mKdV equations are given to show the effectiveness of the coupled VIM–Laplace–Padé and VIM–Padé techniques.