Traveling solitons in long-range oscillator chains

Abstract

Abstract.We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi-Pasta-Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent 1 < α ≤ 3. We obtain an analytic perturbative expression of traveling envelope solitons by introducing a Non Linear Schrödinger (NLS) equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to develop the theory using discrete difference operators. Those properties are also the ultimate reason why kink-solitons may exist but are unstable, at variance with the short-range FPU model. We successfully compare these approximate analytic results with numerical simulations.

Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

“…[7] differs from (5) as the long-range interaction is only in the nonlinear term, while here we consider the case in which the long-range terms are present already in the harmonic limit. Other variants of the model where nonlinearity is local have been considered in the literature [28,29]. Heat transport in a temperature gradient -Nonequilibrium stationary states (NESS's) are studied by attaching reservoirs at temperature T A and T B to the particles in two different regions of the system, A and B, extending over l A and l B lattice sites, respectively (e.g., see Fig 1).…”

Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions

“…Coupled oscillators with power-law LRI were also studied [8][9][10][11][12][13][14][15][16]. The attention was mainly focused on long-range interactions in DNA [8,10], the existence of standing localized solutions like breathers [9], deriving the continuum counterpart of the discrete long-range models, which implies the use of fractional derivatives [11][12][13], weakly chaotic [14] and thermalization [15] properties caused by the long-range character of the interactions and the existence of solitons in a long-range extension of the quartic FPU chain [16].…”

Nonlinear dynamics of damped DNA systems with long-range interactions

“…Our aim in this paper is to study the DNA dynamics taking into account LRI between different DNA base pairs and both Stokes and long-range hydrodynamical damping effects. To address this issue, our analytical study has been inspired by the one recently developed by Miloshevich et al [20] to investigate traveling solitons in long-range oscillator chains. Due to the non analytical properties of the dispersion relation, Miloshevich et al [20] have shown that the discrete difference operator (DDO) technique is more appropriate to study physical systems with LRI.…”