超短电磁脉冲在双谐振介质中的传播
Propagation of extremely short electromagnetic pulses in a doubly-resonant medium
摘要：
在全Maxwell-Duffing-Lorentz模型的框架下研究了超短电磁脉冲在均匀双共振介质中的传播，其中Duffing振子（具有立方非线性的非谐振子）代表介质的介电响应，Lorentz谐振子代表磁响应.波的传播由一维麦克斯韦方程组控制。结果表明，该模型具有单参数族的行波解，其结构为单峰或多峰。解由传播速度参数化。可能的速度的频谱是连续的频谱的下端的一个小的间隔，在其他地方的速度形成一个离散的集合。驼峰的数量和速度之间的相关性建立。行波解是稳定的弱扰动。数值模拟表明，行波脉冲碰撞在一个接近弹性的方式。
英文摘要：
Propagation of extremely short electromagnetic pulses in a homogeneous doubly-resonant medium is considered in the framework of the total Maxwell-Duffing-Lorentz model, where the Duffing oscillators (anharmonic oscillators with cubic nonlinearities) represent the dielectric response of the medium, and the Lorentz harmonic oscillators represent the magnetic response. The wave propagation is governed by the one-dimensional Maxwell equations. It is shown that the model possesses a one-parameter family of traveling-wave solutions with the structure of single or multiple humps. Solutions are parametrized by the velocity of propagation. The spectrum of possible velocities is shown to be continuous on a small interval at the lower end of the spectrum; elsewhere the velocities form a discrete set. A correlation between the number of humps and the velocity is established. The traveling-wave solutions are found to be stable with respect to weak perturbations. Numerical simulations demonstrate that the traveling-wave pulses collide in a nearly elastic fashion.
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