Dynamical system theory is applied to the integrable nonlinear wave equation
)xxx=0. We obtain the single peak solitary wave solutions and
compacton solutions of the equation. Regular compacton solution of the equation correspond
to the case of wave speed c = 0. In the case of c 6= 0, we find smooth soliton
solutions. The influence of parameters of the traveling wave solutions is explored by
using the phase portrait analytical technique. Asymptotic analysis and numerical simulations
are provided for these soliton solutions of the nonlinear wave equation.