0000000000421901
AUTHOR
Timoléon C. Kofané
Chaotic behaviour in deformable models: the asymmetric doubly periodic oscillators
Abstract The motion of a particle in a one-dimensional perturbed asymmetric doubly periodic (ASDP) potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. Theory predicts the regions of chaotic behaviour of orbits in a good agreement with computer calculations.
Nonlinear excitations in a compressible quantum Heisenberg chain
Abstract We investigate, both analytically and numerically, nonlinearly coupled magnetic and elastic excitations of compressible Heisenberg chains. From a shallow water wave treatment of perturbation terms, one can derive two types of coupled equations which are coupled Boussinesq and nonlinear Schrodinger (NLS) equations and coupled Boussinesq and NLS-like equations. We also simulate collisions between magnetic and elastic solitons in the compressible Heisenberg chain when a nonlinearized approach is performed to deal with the magnetic modes in the presence of harmonic as well as anharmonic interactions. Finally, from a fast Fourier transform (FFT) algorithm, the dynamical structure factor…
Chaotic behavior in deformable models: the double-well doubly periodic oscillators
Abstract The motion of a particle in a one-dimensional perturbed double-well doubly periodic potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behavior predicted by the theoretical analysis agree very well with numerical simulations.
Subharmonic and homoclinic bifurcations in the driven and damped sine-Gordon system
Abstract Chaotic responses induced by an applied biharmonic driven signal on the sine-Gordon (sG) system influenced by a constant dc-driven and the damping fields are investigated using a collective coordinate approach for the motion of the breather in the system. For this biharmonic signal, one term has a large amplitude at low frequency. Thus, the classical Melnikov method does not apply to such a system; however, we use the modified version of the Melnikov method to homoclinic bifurcations of the perturbed sG system. Additionally resonant breathers are studied using the modified subharmonic Melnikov theory. This dynamic behavior is illustrated by some numerical computations.
Horseshoe-shaped maps in chaotic dynamics of long Josephson junction driven by biharmonic signals
Abstract A collective coordinate approach is applied to study chaotic responses induced by an applied biharmonic driven signal on the long Josephson junction influenced by a constant dc-driven field with breather initial conditions. We derive a nonlinear equation for the collective variable of the breather and a new version of the Melnikov method is then used to demonstrate the existence of Smale horseshoe-shaped maps in its dynamics. Additionally, numerical simulations show that the theoretical predictions are well reproduced. The subharmonic Melnikov theory is applied to study the resonant breathers. Results obtained using this approach are in good agreement with numerical simulations of …
Long-range effects on the periodic deformable sine-Gordon chains
The model of long-range interatomic interactions is found to reveal a number of new features, closely connected with the substrate potential shape parameter s. The phase trajectories, as well as an analytical analysis, provide information on a disintegration of solitons upon reaching some critical values of the lattice parameters. An implicit form for two classes of these topological solitons (kink) is calculated exactly.
Analytical calculation of the Peierls-Nabarro barriers for the Remoissenet-Peyrard substrate potential
We derive analytically the pinning potential and the pinning barrier of kinks due to discreteness of lattices for the Remoissenet-Peyrard substrate potential by means of the residue method. The theoretical analysis in the low discreteness effect regime is compared in detail with numerical results of Peyrard and Remoissenet [Phys. Rev. B 26, 2886 (1982)], yielding a very satisfactory agreement.