Vishnu Priya N, Senthilvelan M, Lakshmanan M
Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024, Tamil Nadu, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):022918. doi: 10.1103/PhysRevE.88.022918. Epub 2013 Aug 21.
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.
我们给出了双分量非线性薛定谔（NLS）方程，即马纳科夫方程的一般呼吸子（GB）、艾哈迈德耶夫呼吸子（AB）、马孤子（MS）和 rogue 波（RW）解的显式形式。我们通过两种不同的途径推导这些解。在前向途径中，我们首先为该模型构造一个合适的周期包络孤子解，从中我们推导出 GB、AB、MS 和 RW 解。然后我们将 RW 解作为起点，反向推导出 AB、MS 和 GB。到目前为止，第二种方法尚未针对双分量 NLS 方程进行说明。我们的结果表明，马纳科夫系统的上述有理解可以从具有修正非线性参数的标准标量非线性薛定谔方程推导出来。通过这种双向方法，我们对这些有理解有了更广泛的理解，这在各种情况下都将是有意义的。
