  Characterization of self-consistent laser-plasma evolutions serves as a
fundamental issue in the field of relativistic laser-plasma interactions. In
this paper, we present an analysis framework for description of these
evolutions during propagation of a short intense laser pulse in a sub-critical
high-density plasma (the pulse length exceeds the plasma wavelength). In this
context, the pulse evolutions are attributed to the wakefield induced
self-modulation and destabilization via parametric exponentiation of the
initial noise content. The self-consistent plasma evolutions are formulated in
terms of quantities which used to be motion constants in the absence of pulse
evolutions. This proves very useful both in understanding plasma evolutions
during self-modulation and also in facilitating the instability studies in the
strongly nonlinear regime, via refinement of unstable plasma perturbations.
General analytical solutions, at arbitrary pulse conditions, are derived for
self-modulation, indicating that the envelop evolutions are driven by the
induced spatial frequency-chirp. Also, these results state that the envelope
attains fine modulations which produce long wavelength low-frequency modes via
beating the carrier mode. The plasma wave variations are found to convect and
amplify away from the pulse front. Regarding parametric instability, we assess
different scattering regimes at different pulse shapes and peak intensities,
manifesting anomalous behaviors ranging from wild positioning of the Stokes
wave in dispersion plane to broadening in the scattered spectrum and halting
the instability. Our analyses are assisted and verified by numerous fluid and
particle-in-cell simulations. Based on our results, we discuss phenomena like
the pulse breakup and its different regimes, and assisted particle acceleration
in presence of pulse evolutions.
