论文标题
马纳科夫系统中的矢量呼吸器
Vector breathers in the Manakov system
论文作者
论文摘要
从理论上讲，我们研究了在不稳定的波场背景上传播的矢量呼吸器的非线性相互作用。作为模型，我们使用一维焦点非线性Schrodinger方程的两组分扩展-Manakov系统。使用调味料方法，我们为Manakov模型生成了多呼吸道解决方案。如前所述[D。 Kraus，G。Biondini和G. Kovacic，非线性28，310，2015]矢量呼吸器类别由三种基本类型的I，II和III类型提出。它们的相互作用产生了两个组分（偏振）非线性波模式的广泛家族。首先，我们证明了I型和II和III型对应于Manakov系统的分散法的两个不同分支，在不稳定的背景的情况下。然后，我们研究了关键的互动情况，包括站立和移动的呼吸器的碰撞以及共振呼吸转化。对两呼吸器解决方案的分析使我们能够得出一般公式，描述了相互碰撞中呼吸器获得的相位和空间变化。发现的表达使我们能够描述呼吸器相互作用的渐近状态，并将呼吸器的共振融合和衰减解释为在合并呼吸特征值的情况下，是无限空间转移的限制案例。最后，我们证明只有$ \ mathrm {i} $呼吸器参与了从小幅度扰动的调节不稳定性，而$ \ mathrm {ii} $ and $ \ mathrm {ii} $ and $ \ mathrm {iii}的呼吸者的呼吸与稳定的分支相关。
We study theoretically the nonlinear interactions of vector breathers propagating on an unstable wavefield background. As a model, we use the two-component extension of the one-dimensional focusing nonlinear Schrodinger equation -- the Manakov system. With the dressing method, we generate the multi-breather solutions to the Manakov model. As shown previously in [D. Kraus, G. Biondini, and G. Kovacic, Nonlinearity 28, 310, 2015] the class of vector breathers is presented by three fundamental types I, II, and III. Their interactions produce a broad family of the two-component (polarized) nonlinear wave patterns. First, we demonstrate that the type I and the types II and III correspond to two different branches of the dispersion law of the Manakov system in the presence of the unstable background. Then we investigate the key interaction scenarios, including collisions of standing and moving breathers and resonance breather transformations. Analysis of the two-breather solution allows us to derive general formulas describing phase and space shifts acquired by breathers in mutual collisions. The found expressions enable us to describe the asymptotic states of the breather interactions and interpret the resonance fusion and decay of breathers as a limiting case of infinite space shift in the case of merging breather eigenvalues. Finally, we demonstrate that only type $\mathrm{I}$ breathers participate in the development of modulation instability from small-amplitude perturbations within the superregular scenario, while the breathers of types $\mathrm{II}$ and $\mathrm{III}$, belonging to the stable branch of the dispersion law, are not involved in this process.
