NONLINEAR MODULATIONAL INSTABILITY OF PERIODIC-WAVES GOVERNED BY THE KURAMOTO-SIVASHINSKY EQUATION

It is known that spatially periodic waves governed by the Kuramoto-Siv ashinsky equation have an interval of linear stability. However, the n umerical simulations show a spatio-temporal chaos. In the present pape r, the non-linear instability is investigated on the boundaries of the stability interval. The analysis of amplitude equations shows that th e non-linear evolution of finite-amplitude modulational disturbances o n the left boundaries can take the system out from the stability inter val towards the region of smaller wave numbers.