论文标题
关于波数据包的速度和非线性schrödinger方程
On the speed of wave packets and the nonlinear Schrödinger equation
论文作者
论文摘要
对非线性Schrödinger方程给出的弱非线性波数据包的通用理论被重新审视。在群体和相速度非常接近的极限中，进行的多个尺度分析超出了所有订单，表明单个孤子（明亮或黑暗）可以以与组速度不同的速度行驶。在指数型但有限的参数范围内，孤子的信封锁定在载波的快速振荡上。最终，动力学由与摆的方程式持续存在的方程式，其中孤子的质量中心具有周期性的潜力。因此，孤子速度不是恒定的，并且通常包含一个周期性分量。此外，原则上，两个遥远的孤子之间的相互作用可以通过上述有效的周期性潜力深刻改变，我们猜想了新结合状态的存在。这些结果是在广泛的波浪模型上得出的，并以一种普遍的方式得出，以至于它们具有普遍的有效性。
The universal theory of weakly nonlinear wave packets given by the nonlinear Schrödinger equation is revisited. In the limit where the group and phase velocities are very close together, a multiple scale analysis carried out beyond all orders reveals that a single soliton, bright or dark, can travel at a different speed than the group velocity. In an exponentially small but finite range of parameters, the envelope of the soliton is locked to the rapid oscillations of the carrier wave. Eventually, the dynamics is governed by an equation anologous to that of a pendulum, in which the center of mass of the soliton is subjected to a periodic potential. Consequently, the soliton speed is not constant and generally contains a periodic component. Furthermore, the interaction between two distant solitons can in principle be profoundly altered by the aforementioned effective periodic potential and we conjecture the existence of new bound states. These results are derived on a wide class of wave models and in such a general way that they are believed to be of universal validity.
