Space-time chaos in spatially continuous systems

We give the natural definition of space-time chaos for extended dynamical s ystems which are continuous in a (physical) space. Moreover, we show that s uch a type of dynamics exists in nonlinear wave equations with some broad c lasses of potentials. This type of space-time chaos: is different from the space-time mixing which has been extensively studied for discrete in space extended systems (lattice dynamical systems). It rather describes a chaotic change in time of spatial patterns and corresponds to a topological mixing in a functional space. (C) 1999 Elsevier Science B.V. All rights reserved.