Low-frequency discrete breathers in long-range systems without on-site potential

Abstract

A mechanism of long-range couplings is proposed to realize low-frequency discrete breathers without on-site potentials. The realization of such discrete breathers requires a gap below the band of linear eigenfrequencies. Under the periodic boundary condition of a one-dimensional lattice and the limit of large population, we show theoretically that the long-range couplings universally open the gap below the band irrespective of the coupling functions, while the short-range couplings cannot. The existence of the low-frequency discrete breathers, spatial localization, and stability are numerically analyzed from long range to short range.

Nonlinear excitations in magnetic lattices with long-range interactions

“…In addition to our observations in the present paper, our work paves the way towards further studies to explore the nuances of long-range interactions in nonlinear lattice systems. Examples include bistability of solitary waves [32,33], solitary waves with nontrivial phases [31], and low-frequency breathers [35]. These avenues go beyond the confines of mechanical or magnetic systems and are of broad appeal for a variety of long-range phenomena.…”

“…A variety of new studies continue to elucidate fascinating consequences of long-range interactions. For example, recent studies have revealed the emergence of traveling discrete breathers without tails in nonlinear lattices with suitable long-range interactions [34] and the emergence of a linear spectral gap, which enables the emergence of a low-frequency breather [35], in nonlinear lattices with other long-range interactions. Although there are many theoretical and computational studies of lattice systems with long-range interactions, we are not aware of any experimental realizations of breathers in such systems.…”

Discrete Breathers in $$\phi ^4$$ and Related Models

“…Recent work, in fact, brings up the possibility that relevant solutions may fail to exist at higher orders in some important case examples [89]. Studying also long-range interactions may bring about surprises and produce gaps in the spectrum where novel DBs may exist, as per the recent work of [90]. Again, this is a topic meriting further exploration.…”