Priya N Vishnu, 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. 2014 Jun;89(6):062901. doi: 10.1103/PhysRevE.89.062901. Epub 2014 Jun 2.
We construct dark-dark soliton, general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of a coupled generalized nonlinear Schrödinger (CGNLS) equation. While dark-dark solitons are captured in the defocusing regime of the CGNLS system, the other solutions, namely, GB, AB, MS, and RW, are identified in the focusing regime. We also analyze the structures of GB, AB, MS, and RW profiles with respect to the four-wave mixing parameter. We show that when we increase the value of the real part of the four-wave mixing parameter, the number of peaks in the breather profile increases and the width of each peak shrinks. Interestingly, the direction of this profile also changes due to this change. As far as the RW profile is concerned the width of the peak becomes very thin when we increase the value of this parameter. Further, we consider the RW solution as the starting point, derive AB, MS, and GB in the reverse direction, and show that the solutions obtained in both directions match each other. In the course of the reverse analysis we also demonstrate how to capture the RW solutions directly from AB and MS.
我们构造了一个耦合广义非线性薛定谔（CGNLS）方程的暗-暗孤子、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。在 CGNLS 系统的散焦区域捕获了暗-暗孤子，而在聚焦区域识别出了其他解，即 GB、AB、MS 和 RW。我们还针对四波混频参数分析了 GB、AB、MS 和 RW 波形的结构。我们表明，当我们增加四波混频参数实部的值时，呼吸子波形中的峰值数量增加，且每个峰值的宽度变窄。有趣的是，由于这种变化，该波形的方向也会改变。就 RW 波形而言，当我们增加此参数的值时，峰值的宽度会变得非常窄。此外，我们以 RW 解为起点，反向推导 AB、MS 和 GB，并表明在两个方向上获得的解相互匹配。在反向分析过程中，我们还展示了如何直接从 AB 和 MS 中捕获 RW 解。
