  We simulate KdV and dissipation-less Burgers equations using delta-correlated
random noise as initial condition. We observe that the energy fluxes of the two
equations remain zero throughout, thus indicating their equilibrium nature. We
characterize the equilibrium states using Gaussian probability distribution for
the real space field, and using Boltzmann distribution for the modal energy. We
show that the single soliton of the KdV equation too exhibits zero energy flux,
hence it is in equilibrium. We argue that the energy flux is a good measure for
ascertaining whether a system is in equilibrium or not.
