Travelling waves in lattice models of multi-dimensional and multi-component media. I. General hyperbolic properties

The authors 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 ′ 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.