Invariant NNM Manifolds for Studying Localized and Chaotic Dynamics of an Array Composed of STIFF/SOFT Elements

This study concerns propagation of waves in a coupled array of soft/stiff oscillators. We show that the array supports a family of purely slow waves, including a solitary one, and a family of purely fast waves. The slow and fast waves interact to give rise to chaotically modulated slow/fast and fast/slow waves. Slow and fast waves are realized as two-dimensional invariant manifolds (normal modes) in phase space of a singular perturbation problem.