  As galaxy redshift surveys probe deeper into the universe, they uncover ever
more dramatic structures in the large-scale distribution of galaxies. In
particular, the CfA2 and SSRS2 surveys to an apparent magnitude limit of 15.5
exhibit an impressive complex of sheets, filaments, and clusters. The formation
of the large-scale structure in the universe results from the gravitational
amplification of the primordial small perturbations of density. The primordial
density perturbations, as quantum fluctuations at the very early stage, may
reveal important information about the early universe and the laws of
fundamental physics. One of the major obstacles to understanding the formation
of the large-scale structure is the complexity of the evolution of the density
inhomogeneities at the nonlinear stage when the observable structures form. One
way of addressing this problem is to run three-dimensional numerical
simulations. Here we review another approach based on the approximate analytic
model of the nonlinear gravitational instability utilizing Burgers' equation of
the nonlinear diffusion.
