SOLITARY WAVES GENERATED BY INSTABILITIES

The traditional soliton theory deals with integrable dynamical systems possessing an infinite number of conservation laws. However, one observes solitary waves also in physical systems that are not conservative. Such ''solitons'' can be generated spontaneously by an instability of the homogeneous state. In some cases, this phenomenon takes place in nearly integrable systems (e.g., described by slightly perturbed Korteweg-de Vries equation), but solitary waves can exist even in essentially non-conservative systems. The present paper gives a review of some recent investigations of solitary waves and localized states in unstable systems. The main attention is granted to the instabilities in fluids produced by buoyancy and thermocapillary effects. The case of the perturbed Korteweg-de Vries equation is considered in detail.