The fundamental system is transformed to three nonlinear equations of the interacting components, a rightwards propagating, leftwards propagating and stationary one, by a projecting technique. The dynamics is determined by small nonlinear, dispersive and viscous terms. Finally the system is reduced to one equation of Korteweg-de Vries type. It is shown that the evolution is described by an integrable KdV-MKdV equation on a class of initial conditions specified by the projection. A soliton solution is presented. ©2000 American Institute of Physics.