亚光速波子弹：波动方程的精确定域亚光速解
Sub-luminal wave bullets: Exact Localized subluminal Solutions to the Wave Equations
摘要：
在这项工作中，它是如何获得，在一个简单的方式，本地化（非衍射）亚光速脉冲作为精确的解析解的波动方程。这些新的理想的亚光速解，在任何均匀的线性介质中无失真地传播，在此获得任意选择的频率和带宽，特别是避免任何求助于非因果分量，所以频繁地破坏先前已知的局域波。新的解决方案是适当的叠加-零阶，一般-贝塞尔光束，这可以通过积分相对于（w.r.t.）角频率，或者通过积分w.r.t.纵向波数：本文对这两种方法进行了阐述。第一个似乎是足够强大的;我们研究的第二种方法，以及，但是，因为它允许处理，甚至与零速度的解决方案的限制情况下（和deluxes一种新的方式，在连续谱方面，获得所谓的“冻结波”，所以也有希望从应用的角度来看）。我们简要地处理的情况下，此外，非轴对称的解决方案，在高阶贝塞尔光束。最后，特别注意狭义相对论的作用，并注意到这样一个事实，即局域波有望通过适当的洛伦兹变换从一个转换成另一个。具有内禀有限能量或仅被截断的类似脉冲将在另一篇论文中构造。在这篇文章中，我们特别注意电磁学和光学：但是只要波动方程起了重要作用（如在声学、地震学、微物理学、引力、基本粒子物理学等），这类结果就有效。
英文摘要：
In this work it is shown how to obtain, in a simple way, localized (non- diffractive) subluminal pulses as exact analytic solutions to the wave equations. These new ideal subluminal solutions, which propagate without distortion in any homogeneous linear media, are herein obtained for arbitrarily chosen frequencies and bandwidths, avoiding in particular any recourse to the non-causal components so frequently plaguing the previously known localized waves. The new solutions are suitable superpositions of --zeroth-order, in general-- Bessel beams, which can be performed either by integrating with respect to (w.r.t.) the angular frequency, or by integrating w.r.t. the longitudinal wavenumber: Both methods are expounded in this paper. The first one appears to be powerful enough; we study the second method as well, however, since it allows dealing even with the limiting case of zero-speed solutions (and furnishes a new way, in terms of continuous spectra, for obtaining the so-called "Frozen Waves", so promising also from the point of view of applications). We briefly treat the case, moreover, of non-axially symmetric solutions, in terms of higher order Bessel beams. At last, particular attention is paid to the role of Special Relativity, and to the fact that the localized waves are expected to be transformed one into the other by suitable Lorentz Transformations. The analogous pulses with intrinsic finite energy, or merely truncated, will be constructed in another paper. In this work we fix our attention especially on electromagnetism and optics: but results of the present kind are valid whenever an essential role is played by a wave-equation (like in acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.)
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