色散shock waves在nematic liquid crystals中的调制理论和谐振区
Modulation theory and resonant regimes for dispersive shock waves in nematic liquid crystals
摘要：
本文对色散激波在液晶中的传播进行了全面的分析。这些色散冲击波产生的光场的初始条件，并在线性衍射波与DSW共振，导致在它前面传播的共振线性波列共振。它被发现，有六个制度，这是不同的，需要不同的解决方案的方法。在以前的研究中，相同的解决方案的方法被用于所有的制度，这并不产生的解决方案完全符合数值解。事实上，标准DSW结构消失足够大的初始跳跃。渐近理论，近似方法或Whitham调制理论被用来找到这些共振色散冲击波在给定的制度的解决方案。的解决方案被发现是在所有政权的数值解的EQUIPMENT方程非常一致。结果发现，对于小的初始跳跃，共振波列是不稳定的，但它稳定在临界跳跃高度以上。另外还发现，DSW是不稳定的，除了小的跳跃高度，没有共振和大的跳跃高度，没有标准的DSW结构。
英文摘要：
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.
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