Analyticity of global attractors and determining nodes for a class of damped non-linear wave equations

The Gevrey regularity of global attractors of dynamical systems generated by a certain class of coupled dissipative systems of damped non-linear wave equations with periodic boundary conditions is established. This result means that the elements of the attractor are real-analytic functions in the spatial variables. As an application the existence of two determining nodes for the corresponding problem in one spatial dimension is proved.