  The manuscript reports the observation of time dependent localized and
non-propagating structures in the coupled laser plasma system through 1-D fluid
and PIC simulations. It is reported that such structures form spontaneously as
a result of collision amongst certain exact solitonic solutions. They are seen
to survive as coherent entities for a long time up to several hundreds of
plasma periods. Furthermore, it is shown that such time dependence can also be
artificially recreated by significantly disturbing the delicate balance between
the radiation and the density fields required for the exact non-propagating
solution obtained by Esirkepov et al. [1]. The ensuing time evolution is an
interesting interplay between kinetic and field energies of the system. The
electrostatic plasma oscillations are coupled with oscillations in the
electromagnetic field. The inhomogeneity of the background and the relativistic
nature, however, invariably produce large amplitude density perturbations
leading to its wave breaking. In the fluid simulations, the signature of wave
breaking can be discerned by a drop in the total energy which evidently gets
lost to the grid. The PIC simulations are observed to closely follow the fluid
simulations till the point of wave breaking. However, the total energy in the
case of PIC simulations is seen to remain conserved all throughout the
simulations. At the wave breaking the particles are observed to acquire thermal
kinetic energy in the case of PIC. Interestingly, even after wave breaking,
compact coherent structures with trapped radiation inside high-density peaks,
continue to exist both in PIC and fluid simulations. Though the time evolution
does not exactly match in the two simulations as it does prior to the process
of wave breaking, the time-dependent features exhibited by the remnant
structures are characteristically similar.
