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On the simulation of the energy transmission in the forbidden band-gap of a spatially discrete double sine-Gordon system

机译：关于空间离散双正弦-Gordon系统禁带隙中能量传输的模拟

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摘要

In this work, we present a numerical method to consistently approximate solutions of a spatially discrete, double sine-Gordon chain which considers the presence of external damping. In addition to the finite-difference scheme employed to approximate the solution of the difference-differential equations of the model under investigation, our method provides positivity-preserving 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 sine-Gordon and coupled double sine-Gordon chains. Secondly, the method is used in the investigation of the phenomenon of nonlinear transmission of energy in double sine-Gordon systems; the qualitative effects of the damping coefficient on the occurrence of the nonlinear process of supratransmission are briefly determined in this work, too.
机译：在这项工作中，我们提出了一种数值方法来一致地近似考虑存在外部阻尼的空间离散双正弦-Gordon链的解。除了采用有限差分方案来近似所研究模型的差分方程式的解外，我们的方法还提供了一个保正方案来近似系统的局部能量和总能量，使得总能量相对于时间的离散变化率提供了相应连续变化率的一致近似值。首先进行仿真，以针对耦合正弦-戈登链和耦合双正弦-戈登链的已知定性解评估计算技术的有效性。其次，该方法用于研究双正弦-戈登系统中能量的非线性传递现象。这项工作还简要地确定了阻尼系数对超传输非线性过程发生的定性影响。

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