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 ϕi=0 or π (standard configurations). In this Letter we prove that in this kind of systems, the standard configurations are the only possible ones, so phase-shift breathers (configurations with ϕi≠0, π) cannot be supported. This fact also determines the linear stability of the existing multibreathers.