Discrete breathers: Exact solutions in piecewise linear models

Exact breather solutions are constructed in piecewise linear (PWL) versions of the discrete nonlinear Schrodinger and Klein-Gordon equations. These so lutions correspond to intersections of stable and unstable manifolds of rel evant fixed points in associated 2D mappings, an exact construction of whic h is possible due to the PWL nature of the models. Such exact solutions giv e us insight into several aspects of breather properties. The problem of dy namical stability of the breathers is mentioned as an instance, detailed re sults on which will be presented in a future paper.