In this paper we like to explore the full power of Adomian decomposition method (ADM) to solve nonlinear problems.  ADM has the capability to obtain three different types of solutions, namely explicit exact solution, analytic solution and semi-analytic solution. When a closed form solution exists, ADM is possible to capture this explicit solution, while most of the numerical methods can only get approximation, not exact solution.  On the other hand, ADM is itself a computational method for solution, while the method of characteristics needs assistance from other numerical methods to find characteristic curve and differential equation on it.  We will demonstrate ADM to solve the prototype nonlinear PDEs, i.e. the inviscid and viscous Burgers' equations with source term and parameter, and conclude the superior of ADM.