Revista mexicana de física
Print version ISSN 0035-001X
MACIAS-DIAZ, J.E.. Computer simulation of the energy dynamics of a sinusoidally perturbed double sine-Gordon equation: an application to the transmission of wave signals. Rev. mex. fis. [online]. 2012, vol.58, n.1, pp. 29-40. ISSN 0035-001X.
In this work, we employ a numerical method to approximate the solutions of a damped, double sine-Gordon equation spatially defined over a closed and bounded interval of the real line, subject to a harmonic perturbation of the Dirichlet type on one end, and a homogeneous Neumann condition on the other. The method has schemes to approximate consistently the temporal dynamics of the local energy density and the total energy of the medium, and the total energy over any finite interval of time and, additionally, it preserves the positivity of the corresponding energy operators. As an application of this method, we establish numerically that the phenomenon of nonlinear bistability (which is physically characterized by the coexistence of conducting and insulating regimes) is present in media governed by damped, double sine-Gordon equations when the systems are driven harmonically at a frequency in the forbidden band-gap. We employ this nonlinear process in order to accurately propagate localized pulses from the perturbed end to the free boundary. Two different methods for the transmission of monochromatic waves are employed in this study, and our results demonstrate that an efficient propagation of information is feasible, indeed.
Keywords : Double sine-Gordon equation; computer simulation; nonlinear bistability; wave propagation; signal transmission.