Exact solution to Duffing equation and the pendulum equation

In this work we obtain an exact solution to cubic Duffing oscillator equation with initial conditions and bounded periodic solutions. This solution is expressed in terms of the Jacobi elliptic function cn. In particular, we may apply the exact solution in the study of the cubic nonlinear Schrodinger equation, which is reduced to a cubic Duffing oscillator equation by means of a traveling wave transformation.