Transfer Loop and Statistical Equilibrium of Korteweg-de Vries-Burgers Systems Associated to Classical Nonlinear Acoustics and Quantum Shock Waves

Abstract

We propose and demonstrate, with the one-dimensional Korteweg-de Vries-Burgers model, the scenarios of transfer loop and \textit{all-scale} statistical equilibrium, the former being associated to shock formation and the latter to Gaussian distributions as in a canonical ensemble, but with wavelength-dependent temperatures. The discussions emphasize, among the multi-disciplinary relevance, the classical nonlinear acoustics and quantum shock waves, for the possibility of more favorable experimental tests.

arXiv commenttypos, especially the one in the dispersion term of equation 1, are corrected; figures replaced with eps files with vector render type for higher quality (when zoomed in)