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

TL;DR

This paper proves that one-dimensional Klein-Gordon lattices with nearest-neighbor interactions cannot support phase-shift breathers, only standard configurations with phase differences of 0 or π, which also determines their linear stability.

Contribution

It establishes the non-existence of phase-shift breathers in these lattices, clarifying the limitations of multibreather configurations.

Findings

Only standard multibreather configurations are possible.

Phase-shift breathers cannot exist in these systems.

The stability of multibreathers is determined by this non-existence.

Abstract

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.