论文标题
关于马纳科夫的渐近动力学制度，$ n $ -soliton火车绝热近似
On Asymptotic Dynamical Regimes of Manakov $N$-soliton Trains in Adiabatic Approximation
论文作者
论文摘要
我们分析了马纳科夫模型绝热近似中的$ n $ soliton列车的动态行为。受益/损失效应以及几种类型的外部电位的扰动％。 Manakov $ n $ -soliton火车的演变由复杂的TODA链（CTC）描述，该链（CTC）是一个完全可以整合的动力学模型。计算其宽松基质的特征值使我们能够确定每个孤子的渐近速度。因此，我们描述了一组孤子参数，这些参数确保了两种主要类型的渐近状态之一：结合状态状态（BSR）和自由渐近状态（FAR）。特别是，我们找到了$ n $ solitons的特殊对称配置的明确说明，这些配置可确保BSR和远。我们发现，CTC预测的孤子轨迹与从Manakov系统计算出的孤子轨迹之间的出色匹配，用于广泛的孤子参数。这证实了我们模型的有效性。
We analyze the dynamical behavior of the $N$-soliton train in the adiabatic approximation of the Manakov model. %perturbed by gain/loss effects and also by several types of external potentials. The evolution of Manakov $N$-soliton trains is described by the complex Toda chain (CTC) which is a completely integrable dynamical model. Calculating the eigenvalues of its Lax matrix allows us to determine the asymptotic velocity of each soliton. So we describe sets of soliton parameters that ensure one of the two main types of asymptotic regimes: the bound state regime (BSR) and the free asymptotic regime (FAR). In particular we find explicit description of special symmetric configurations of $N$ solitons that ensure BSR and FAR. We find excellent matches between the trajectories of the solitons predicted by CTC with the ones calculated numerically from the Manakov system for wide classes of soliton parameters. This confirms the validity of our model.
