Non-Existence of phase-shift breathers in one-dimensional Klein-Gordon lattices with nearest-neighbor interactions

It is well known that one-dimensional Klein-Gordon lattices with nearest-neighbor interactions can support multibreathers with phase differences between the successive "central" oscillators $\phi_i=0\ \mbox{or}\ \pi$ (standard configurations). In this paper we prove that in this kind of systems, the standard configurations are the only possible ones, so phase-shift breathers (configurations with $\phi_i\neq0,\, \pi$) cannot be supported. This fact also determines the linear stability of the existing multibreathers.