Travelling waves near a critical point of a binary fluid mixture

Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to an universal form of the free energy near critical conditions and can be integrated by a rescaling process where the binary mixture is similar to a single fluid. Nevertheless, density solution profiles obtained are not necessarily monotonic. The results of this paper might be extended to other topics like in finance or biology.