Optique Nonlinéaire Théorique, Université libre de Bruxelles (U.L.B.), CP 231, Belgium.
Phys Rev E. 2023 Jan;107(1-1):014219. doi: 10.1103/PhysRevE.107.014219.
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 analogous 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.
重新考察了由非线性薛定谔方程给出的弱非线性波包的通用理论。在群速度和相速度非常接近的极限下，超越所有阶次的多尺度分析表明，单个孤子（亮孤子或暗孤子）可以以不同于群速度的速度传播。在一个指数小但有限的参数范围内，孤子的包络被锁定到载波的快速振荡。最终，动力学由类似于摆的方程控制，其中孤子的质心受到周期性势的作用。因此，孤子速度不是恒定的，通常包含周期性分量。此外，两个远距离孤子之间的相互作用原则上可以通过上述有效周期性势被深刻地改变，我们推测存在新的束缚态。这些结果是在广泛的波模型类上推导出来的，并且以如此普遍的方式，它们被认为具有普遍的有效性。
