Breather initial profiles in networks of weakly coupled anharmonic oscillators

Qualitative information about breather initial profiles in the weak coupling limit of a chain of identical one-dimensional anharmonic oscillators is found by studying the linearized equations of motion at a one-site breather. In particular, information is found about how the breather initial profile depends on its period T. Numerical work shows two different kinds of breathers to exist and to occur in alternating T-bands. Genericity of certain aspects of the observed behaviour is proved.