Salerno M, Malomed BA, Konotop VV
Dipartimento di Scienze Fisiche and Istituto Nazionale di Fisica della Materia (INFM), Universita di Salerno, I-84081, Baronissi (SA), Italy.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Dec;62(6 Pt B):8651-6. doi: 10.1103/physreve.62.8651.
Propagation of a shock wave (SW), converting an energy-carrying domain into an empty one, is studied in a discrete version of the normal-dispersion nonlinear Schrodinger equation with viscosity, which may describe, e.g., an array of optical fibers in a weakly lossy medium. It is found that the SW in the discrete model is stable, as well as in its earlier studied continuum counterpart. In a strongly discrete case, the dependence of the SWs velocity upon the amplitude of the energy-carrying background is found to obey a simple linear law, which differs by a value of the proportionality coefficient from a similar law in the continuum model. For the underdamped case, the velocity of the shock wave is found to be vanishing along with the viscosity constant. We argue that the latter feature is universal for long but finite systems, both discrete and continuum. The dependence of the SW's width on the parameters of the system is also discussed.
研究了在具有粘性的正常色散非线性薛定谔方程的离散版本中，冲击波（SW）的传播，该冲击波将携带能量的区域转换为空区域，此方程可描述例如弱损耗介质中的光纤阵列。研究发现，离散模型中的SW是稳定的，其早期研究的连续对应模型中的SW也是稳定的。在强离散情况下，发现SW速度对携带能量背景振幅的依赖性遵循简单的线性定律，该定律与连续模型中类似定律的比例系数值不同。对于欠阻尼情况，发现冲击波速度随着粘性常数消失。我们认为，后一特征对于长但有限的系统（离散和连续系统）是普遍的。还讨论了SW宽度对系统参数的依赖性。
