论文标题
列液晶的分散性冲击波的调制理论和共振状态
Modulation theory and resonant regimes for dispersive shock waves in nematic liquid crystals
论文作者
论文摘要
对列液晶中的所有光学色散冲击波（DSW）传播的所有制度进行了完整分析。这些色散冲击波是从光场的步骤初始条件产生的，并且具有共鸣，因为线性衍射波与DSW产生共鸣，从而导致在其前面传播的共振线性波动。发现有六个方案，它们是不同的，需要不同的解决方案方法。在先前的研究中，所有制度都使用了相同的解决方案方法，该方法与数值解决方案完全不一致。实际上，标准DSW结构消失了，以进行足够大的初始跳跃。渐近理论，近似方法或WHITHAM调制理论用于在给定的方案中找到这些共振分散性冲击波的解。发现该解决方案与所有制度中的列式方程的数值解决方案非常吻合。已经发现，对于小初始跳跃，谐振波形是不稳定的，但是它可以稳定在临界跳跃高度以上。还发现，DSW不稳定，除了没有共鸣和没有标准DSW结构的大型跳跃高度。
A full analysis of all regimes for optical dispersive shock wave (DSW) propagation in nematic liquid crystals is undertaken. These dispersive shock waves are generated from step initial conditions for the optical field and are resonant in that linear diffractive waves are in resonance with the DSW, resulting in a resonant linear wavetrain propagating ahead of it. It is found that there are six regimes, which are distinct and require different solution methods. In previous studies, the same solution method was used for all regimes, which does not yield solutions in full agreement with numerical solutions. Indeed, the standard DSW structure disappears for sufficiently large initial jumps. Asymptotic theory, approximate methods or Whitham modulation theory are used to find solutions for these resonant dispersive shock waves in a given regime. The solutions are found to be in excellent agreement with numerical solutions of the nematic equations in all regimes. It is found that for small initial jumps, the resonant wavetrain is unstable, but that it stabilises above a critical jump height. It is additionally found that the DSW is unstable, except for small jump heights for which there is no resonance and large jump heights for which there is no standard DSW structure.
