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