On the simulation of the energy transmission in the forbidden bandgap of a spatially discrete double sineGordon system
Abstract
In this work, we present a numerical method to consistently approximate solutions of a spatially discrete, double sineGordon chain which considers the presence of external damping. In addition to the finitedifference scheme employed to approximate the solution of the differencedifferential equations of the model under investigation, our method provides positivitypreserving schemes to approximate the local and the total energy of the system, in such a way that the discrete rate of change of the total energy with respect to time provides a consistent approximation of the corresponding continuous rate of change. Simulations are performed, first of all, to assess the validity of the computational technique against known qualitative solutions of coupled sineGordon and coupled double sineGordon chains. Secondly, the method is used in the investigation of the phenomenon of nonlinear transmission of energy in double sineGordon systems; the qualitative effects of the damping coefficient on the occurrence of the nonlinear process of supratransmission are briefly determined in this work, too.
 Publication:

Computer Physics Communications
 Pub Date:
 November 2010
 DOI:
 10.1016/j.cpc.2010.07.007
 arXiv:
 arXiv:1112.0595
 Bibcode:
 2010CoPhC.181.1842M
 Keywords:

 Mathematical Physics;
 Mathematics  Numerical Analysis;
 Physics  Computational Physics;
 02.60.Lj;
 02.70.Bf;
 45.10.b
 EPrint:
 Computer Physics Communications 181(11), pp. 18421849, 2010