Theory of the Structure of Wave Fronts in Dispersive Dissipative Media.

Using the Korteweg-de Vries-Burgers equation as a model the structure of wave fronts in dispersive media with weak dissipation is considered. The distribution of the motion properties across such fronts is of oscillatory nature. A nonlinear equation of Burgers type is derived for spatially smoothed quantities for the case where the number of oscillations in the front is high. It is shown that the effective viscosity figuring in this equation can be several orders higher than the actual one. Within the framework of a semiempirical approach certain formulas for the effective viscosity are proposed. A comparison is made with the results of numerical and analytical calculations of the initial (unsmoothed) equation in both the steady and unsteady stages.