论文标题
扭结，孤子和冲击串联连接离散的约瑟夫传输线
The kinks, the solitons and the shocks in series connected discrete Josephson transmission lines
论文作者
论文摘要
我们分析研究了由约瑟夫森连接（JJ）和电容器构建的离散约瑟夫森传输线（JTL）中的局部运行波。准核能近似将运行波性质的计算降低到电势场中弹性杆平衡的问题。进行额外的近似值，我们将问题减少到潜在井中虚拟牛顿粒子的运动。我们表明，有超音速扭结和孤子的形式存在跑步波，并计算其速度和轮廓。我们表明，Korteweg-de Vries方程描述了在均质非零背景上的小扰动的非平稳平滑波，而在零背景的情况下，通过修改的Korteweg-de Vries方程来描述。我们还研究了耗散对JTL中运行波的影响，并发现在存在电阻的情况下，与地面电容器串联结合JJ和/或串联，唯一可能的固定运行波是冲击波，也发现了其轮廓。最后，在股票扩张的框架中，我们研究了离散JTL中的非线性分散和调制稳定性。
We analytically study the localized running waves in the discrete Josephson transmission lines (JTL), constructed from Josephson junctions (JJ) and capacitors. The quasi-continuum approximation reduces calculation of the running wave properties to the problem of equilibrium of an elastic rod in the potential field. Making additional approximation, we reduce the problem to the motion of the fictitious Newtonian particle in the potential well. We show that there exist running waves in the form of supersonic kinks and solitons and calculate their velocities and profiles. We show that the nonstationary smooth waves which are small perturbations on the homogeneous non-zero background are described by Korteweg-de Vries equation, and those on zero background -- by modified Korteweg-de Vries equation. We also study the effect of dissipation on the running waves in JTL and find that in the presence of the resistors, shunting the JJ and/or in series with the ground capacitors, the only possible stationary running waves are the shock waves, whose profiles are also found. Finally in the framework of Stocks expansion we study the nonlinear dispersion and modulation stability in the discrete JTL.
