  A time dependent variational approach is used to derive the equations of
motion for the \lambda \phi^4 model. The simultaneous evolution of the quantum
fluctuations and of the classical part of the field is considered in a lattice
of 1+1 dimensions. Different initial conditions corresponding to non
equilibrium situations are considered and evolved in time. Such high energy
localized configurations expand in the lattice by ``bumps'' which may change
with time. The quantum fluctuations make the peaks be smoother and the
expansion faster.
