TRAVELING WAVES IN LATTICE MODELS OF MULTIDIMENSIONAL AND MULTICOMPONENT MEDIA .1. GENERAL HYPERBOLIC PROPERTIES

We study the stability of motion in the form of travelling waves in lattice models of unbounded multi-dimensional and multi-component media with a nonlinear prime term and small coupling depending on a finite number of space coordinates. Under certain conditions on the nonlinear term we show that the set of travelling waves running with the same sufficiently large velocity forms a finite-dimensional submanifold in infinite-dimensional phase space endowed with a special metric with weights. It is 'almost' stable and contains a finite-dimensional strongly hyperbolic subset invariant under both evolution operator and space translations.