论文标题
通过平面波初始条件在阻尼和AC驱动的NLS方程中令人兴奋的极端事件
Exciting extreme events in the damped and AC-driven NLS equation through plane wave initial conditions
论文作者
论文摘要
我们通过直接数值模拟研究了在存在时间周期性强迫和某些参数方案的情况下阻尼和强迫非线性Schrödinger（NLS）方程的动力学。因此，揭示了平面波的初始条件的波数决定了调制不稳定性早期阶段出现的经过易生的流氓波的数量。这些事件的形成产生了相同数量的瞬时“三角”时空模式，每种模式都让人联想到在其半经典限制的动力学中出现的一种时，并补充了消失的初始条件。我们发现，空间衍生物的$ l^2 $ norm和$ l^4 $ - norm在其进化中发现了流氓波的外观。还讨论了初始条件对上述行为的各种参数和嘈杂的扰动的影响。在可观察到的极端波事件的参数状态下，长期行为是根据系统所具有的全局吸引子和空间均匀连续波解的渐近轨道稳定性来解释的。
We investigate, by direct numerical simulations, the dynamics of the damped and forced nonlinear Schrödinger (NLS) equation in the presence of a time periodic forcing and for certain parametric regimes. It is thus revealed, that the wave-number of a plane-wave initial condition dictates the number of emerged Peregrine type rogue waves at the early stages of modulation instability. The formation of these events gives rise to the same number of transient "triangular" spatio-temporal patterns, each of which is reminiscent of the one emerging in the dynamics of the integrable NLS in its semiclassical limit, when supplemented with vanishing initial conditions. We find that the $L^2$-norm of the spatial derivative and the $L^4$-norm detect the appearance of rogue waves as local extrema in their evolution. The impact of the various parameters and noisy perturbations of the initial condition in affecting the above behavior is also discussed. The long time behaviour, in the parametric regimes where the extreme wave events are observable, is explained in terms of the global attractor possessed by the system and the asymptotic orbital stability of spatially uniform continuous wave solutions.
