Explicit solutions for ballistic aggregation of dust-like matter, whose particles stick inelastically upon collisions, are considered. This system provides a model of large-scale structure formationâ€¦ (More)

This work is devoted to the decay of random solutions of the unforced Burgers equation in one dimension in the limit of vanishing viscosity. The initial velocity is homogeneous and Gaussian with aâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2005

This paper continues earlier investigations of the decay of Burgers turbulence in one dimension from Gaussian random initial conditions of the power-law spectral type E0(k) approximately |k|(n).â€¦ (More)

We study the statistical properties of solutions to Burgersâ€™ equation, vt+ vvx = Î½vxx, for large times, when the initial velocity and its potential are stationary Gaussian processes. The initialâ€¦ (More)

The solution of Burgers' equation with random initial conditions is often said to describe "Burgers turbulence." The Burgers equation describes two fundamental effects characteristic of anyâ€¦ (More)

A brief review is given of the nonlinear phenomena arising in the evolution of random perturbations in particle fluxes of the hydrodynamical type, the velocity field of which is described byâ€¦ (More)

We investigate the stability of large-scale structures in Burgers' equation under the perturbation of high wave-number noise in the initial conditions. Analytical estimates are obtained for randomâ€¦ (More)

The evolution of a planar perturbation in a Einstein-de Sitter Universe is studied using a previously introduced Lagrangian scheme. An approximate discrete dynamical system is derived, whichâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2014

The evolution of random nonlinear waves (high-intensity noise) in a dissipative and dispersive media is studied. To describe wave processes, the mathematical model in the form of a nonlinearâ€¦ (More)