Soliton-like excitations in a deformable spin model

Abstract

Nonlinear excitations in a one-dimensional deformable, discrete, classical, ferromagnetic chain are numerically investigated. In the continuum limit the equations of motion are reduced to a Klein-Gordon equation, with a Remoissenet-Peyrard substrate potential. From a numerical computation of the discrete system with a suitable choice of the deformability parameters, the soliton solutions are shown to exist and move both with a monotonic oscillating (i.e. nanopteron) and a monotonic nonoscillating tail, and also with a nonoscillating tail but with a splitting propagating shape. The stability of all these various soliton shapes is confirmed numerically in a range of the reduced magnetic fields greater than for a rigid magnetic chain i.e. 0 b 0.33. From a kink-antikink and a kink-kink colliding simulation, we found various effects, including a bound state of a kink and an antikink, as well as a moving kink profile with higher topological charge that appears to be the bound state of two kinks. For some values of the deformability parameter, with a suitable choice of the initial velocity, we observed that the presence of an internal mode leads to the combination of an attractive and a repulsive phenomenon, that arises when the kink-kink collision is engaged. The fact that this collision happens only in the centre of the magnetic chain with the presence of a minimal distance between the two kinks as long as the collision is produced is also a feature of the deformability effect in the dynamics of a magnetic chain. From our results, it appears that the value of the shape parameter of the substrate potential or the modified Zeeman energy is a factor of utmost importance when modelling magnetic chains.

Synchronization and information transmission in spatio-temporal networks of deformable units

“…In this work, V (x, r) is a nonlinear potential with a deformable shape introduced by Remoissenet-Payrard to study the coherent structure in a network formed by a similar system. There are many versions of this potential, but we concentrate our analyses on the most general case defined as [2][3][4][5][6][7][8] V (x, r) = (1 − r) 2 1 − cos x 1 + r 2 + 2r cos x ,…”

“…The sine-Gordon potential and similar others have been used to model the dynamics of many systems in physics, biology and engineering [1][2][3][4][5][6][7][8]. However, in real physical systems, the shape of the substrate potential can deviate from the standard one with a direct incidence on the stability properties of the system.…”

“…In physical situations, such as charge-density waves, Josephson junctions, or crystals with dislocations, the application of the standard sine-Gordon model becomes too restrictive. In recent years, a number of potentials whose shapes can be turned at wish have appeared in the literature of nonlinear dynamical systems [2][3][4][5][6][7][8]. These more realistic potentials certainly provide richer insights into the physics of real systems than what is predicted using the conventional, rigid models such as the sine-Gordon, double-sine-Gordon and φ 4 potentials.…”