Biondini Gino, Li Sitai, Mantzavinos Dionyssios
Department of Physics, State University of New York at Buffalo, Buffalo, New York 14260, USA.
Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260, USA.
Phys Rev E. 2016 Dec;94(6-1):060201. doi: 10.1103/PhysRevE.94.060201. Epub 2016 Dec 23.
We characterize the properties of the asymptotic stage of modulational instability arising from localized perturbations of a constant background, including the number and location of the individual peaks in the oscillation region. We show that, for long times, the solution tends to an ensemble of classical (i.e., sech-shaped) solitons of the focusing nonlinear Schrödinger equation (as opposed to the various breatherlike solutions of the same equation with a nonzero background). We also confirm the robustness of the theoretical results by comparing the analytical predictions with careful numerical simulations with a variety of initial conditions, which confirm that the evolution of modulationally unstable media in the presence of localized initial perturbations is indeed described by the same asymptotic state.
我们刻画了由恒定背景的局部扰动引起的调制不稳定性渐近阶段的性质，包括振荡区域中各个峰值的数量和位置。我们表明，在长时间情况下，解趋向于聚焦非线性薛定谔方程的一组经典（即 sech 型）孤子（与具有非零背景的同一方程的各种类呼吸子解相反）。我们还通过将解析预测与针对各种初始条件的仔细数值模拟进行比较，证实了理论结果的稳健性，这些模拟证实了在存在局部初始扰动的情况下，调制不稳定介质的演化确实由相同的渐近状态描述。
