Akhmediev breathers, Ma solitons, and general breathers from rogue waves: a case study in the Manakov system.
Akhmediev breathers, Ma solitons, and general breathers from rogue waves: a case study in the Manakov system.
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DOI：
10.1103/physreve.88.022918
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
N. Vishnu Priya;M. Senthilvelan;M. Lakshmanan
中科院分区：
文献类型：
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作者：
N. Vishnu Priya;M. Senthilvelan;M. Lakshmanan
给出了两分量非线性薛定谔方程（即Manakov方程）的一般呼吸子（GB）、Akhmediev呼吸子（AB）、Ma孤子（MS）和流氓波（RW）解的显式形式.我们通过两种不同的途径得到这些解。在前向路径中，我们首先构造了一个合适的周期包络孤子解，并由此导出了GB，AB，MS和RW解。然后，我们考虑RW解决方案作为起点，并推导AB，MS和GB在相反的方向。第二种方法迄今为止还没有说明的两个组件NLS方程。我们的结果表明，上述Manakov系统的有理解可以从标准标量非线性薛定谔方程与修改的非线性参数。通过这种双向的方法，我们建立了一个更广泛的理解这些合理的解决方案，这将是在各种情况下的利益。
We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of the two-component nonlinear Schrödinger (NLS) equation, namely Manakov equation. We derive these solutions through two different routes. In the forward route, we first construct a suitable periodic envelope soliton solution to this model from which we derive GB, AB, MS, and RW solutions. We then consider the RW solution as the starting point and derive AB, MS, and GB in the reverse direction. The second approach has not been illustrated so far for the two component NLS equation. Our results show that the above rational solutions of the Manakov system can be derived from the standard scalar nonlinear Schrödinger equation with a modified nonlinearity parameter. Through this two-way approach we establish a broader understanding of these rational solutions, which will be of interest in a variety of situations.