Multibreathers in Klein-Gordon chains with interactions beyond nearest neighbors

TL;DR

This paper investigates the existence, stability, and bifurcations of multibreathers in Klein-Gordon chains with long-range interactions, revealing new phase configurations and symmetry-breaking phenomena beyond nearest-neighbor models.

Contribution

It introduces a general framework for analyzing long-range interactions in Klein-Gordon chains and uncovers novel multibreather configurations and bifurcations not seen in nearest-neighbor models.

Findings

Long-range interactions modify multibreather phase profiles.

Spontaneous symmetry breaking occurs in multibreather states.

Analytical predictions match numerical simulations very well.

Abstract

We study the existence and stability of multibreathers in Klein-Gordon chains with interactions that are not restricted to nearest neighbors. We provide a general framework where such long range effects can be taken into consideration for arbitrarily varying (as a function of the node distance) linear couplings between arbitrary sets of neighbors in the chain. By examining special case examples such as three-site breathers with next-nearest-neighbors, we find {\it crucial} modifications to the nearest-neighbor picture of one-dimensional oscillators being excited either in- or anti-phase. Configurations with nontrivial phase profiles, arise, as well as spontaneous symmetry breaking (pitchfork) bifurcations, when these states emerge from (or collide with) the ones with standard (0 or $\pi$) phase difference profiles. Similar bifurcations, both of the supercritical and of the subcritical type emerge when examining four-site breathers with either next-nearest-neighbor or even interactions with the three-nearest one-dimensional neighbors. The latter setting can be thought of as a prototype for the two-dimensional building block, namely a square of lattice nodes, which is also examined. Our analytical predictions are found to be in very good agreement with numerical results.