The paper investigates the nonlinear evolution of complex signals and structures having two significantly different scales at the input: a high-frequency noise carrier and a regular modulating function. Consideration of the statistical characteristics of the velocity field is based on the asymptotic solution of the Burgers equation for a vanishingly small viscosity. This solution coincides with the weak solution of the Riemann equation (Hopf equation) and is known as the Oleinik-Laks absolute minimum principle. In this case, the solution of the partial differential equation is reduced to the procedure for finding the absolute minimum of some functional of the initial perturbation, which depends on the coordinate of the observation point and time. The problem of analyzing the statistical characteristics of the velocity and density fields of a one-dimensional flow of inelastically sticking particles is also considered on the basis of the global principle (E-Rykov-Sinai principle). In the special case of a constant initial density, this solution coincides with the Oleinik-Laks absolute minimum principle. In media without dispersion, the multiple interaction of harmonics leads to a strong distortion of the wave profile and the formation of discontinuities, and at long times the field is transformed into a sequence of triangular pulses with the same slope. It is shown that only a relative decrease in modulation occurs for a noise carrier, in contrast to a quasi-monochromatic wave, where, due to nonlinear effects, amplitude modulation is completely suppressed at the stage of developed discontinuities. The statistical characteristics of the velocity and density fields at long times are found, and the process of generating the mean field from a modulated signal perturbation with zero mean at the input is studied. It is shown that if the correlation scale of the noise filling is much smaller than the duration of the localized modulating function, then a practically deterministic signal is formed at large times. On the basis of the global principle, the problems of the escape of particles from a localized bunch with a random input field into free space and the evolution of a flow of particles with random velocities and harmonic modulation of the initial density are analytically considered. It is shown that at long times in both cases the average density field has a universal character. The analytical consideration is compared with the results of numerical simulation, which was carried out on the basis of the Fast Legendre transform algorithm.