Dynamical solitons in a one-dimensional nonlinear diatomic chain

Abstract

Solitonlike excitations with frequencies in the gap of a linear spectrum are considered for a diatomic chain with small mass difference. It is shown that these excitations represent themselves as a complicated combination of solitons of the acoustic and quasioptical branches of the spectrum. The evolution of these solutions is studied in the phase plane and analytical expressions are obtained. The situation is general for systems having two interacting fields with the same nonlinearity but with different dispersion signs.

Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap

“…It is important to find the transient response of the specific linear system with the boundary conditions that are close to a harmonic excitation with frequencies within the band-gap (resulting in an evanescent wave) to identify a characteristic spatial scale where the band-gap is able to affect the shape of the propagating pulse. 4 Linear chain with a static force F 0 = 2.38 N. The top PTFE sphere was given an initial velocity of 0.00442 m/s. a Dynamic force between the top PTFE particle and stainless steel cylinder and b its Fourier spectrum; c dynamic force pulse inside 5th particle (PTFE) (averaged of contact forces between 4th (SS) and 5th (PTFE) and 5th (PTFE) and 6th (stainless steel cylinder) particles) and d its Fourier spectrum; e dynamic force in transmitted pulse inside 11th (PTFE) particle and f its Fourier spectrum It should be mentioned that the existence of a band-gap does not address the question about the distance it takes for the entering signal to be affected by it.…”

“…This is because the frequency band-gaps affect the behavior of the system by prohibiting the propagation of acoustic waves in this part of the frequency spectrum [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Previous theoretical investigations have focused on frequency band-gaps [1][2][3][4][5], localized modes [6,7] or discrete gap breathers [8,9] in discrete linear and weakly nonlinear dynamic systems with various interaction laws between particles.…”

Phase Space Analysis and Soliton Solution for Quartic Potential

“…Although the nonlinearity breaks the symmetry, we make the following ansatz under the condition of weak nonlinearity according to Refs. [3,16,17] = −1 2 , = 2 ; = (−1) 2 +1 , = 2 ………(2.8) This means that the particle displacement is split into two fields by introducing different variables for heavy and lightatom oscillations. Then Equation(2.7) can be rewritten as…”

“…Since the work of Sievers and Takeno [1] reported a kind of intrinsic localized modes in a homogenous nonlinear monoatomic chain in 1988, there has been a substantial and increasing interest in the study of such modes for other similar physical systems [2,3], especially for the nonlinear diatomic chain [4,[5][6][7][8][9]. Although the diatomic chain is one of the simplest physical models, it is related to many real physical systems such as two-component hydrogen-bonded dimers [10,11], oxidicperovskite ferroelectric crystals (e.g.…”

“…along the (100) direction [12], and the Josephson superlattice [13]. Strongly localized anharmonic modes can occur in a perfect diatomic chain when a quartic term is added to the harmonic potential to characterize the nearest-neighbor restoring force between particles [4,6], and the localized modes are different from those of monoatomic chain [14] with the nearest-neighbor interaction nonlinearity.…”