Self-trapping of traveling-wave pulses in binary mixture convection

Localized traveling-wave trains (LTW) have been observed in various experiments on binary mixture convection. I show that the commonly used complex Ginzburg-Landau equations, which fail to describe a characteristic feature of LTW---their extremely slow drift---break down in these systems and I derive a new set of coupled equations which takes into account the slow dynamics of the concentration field. It possesses slow LTW over a wide range of parameters. In addition, it supports LTW even if it has only real coefficients and is therefore far from the nonlinear Schr\"odinger limit.