Chakraborty Sushmita, Nandy Sudipta, Barthakur Abhijit
Department of Physics, Cotton College Guwahati, Guwahati-781001, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Feb;91(2):023210. doi: 10.1103/PhysRevE.91.023210. Epub 2015 Feb 24.
We investigate coupled nonlinear Schrödinger equations (NLSEs) with variable coefficients and gain. The coupled NLSE is a model equation for optical soliton propagation and their interaction in a multimode fiber medium or in a fiber array. By using Hirota's bilinear method, we obtain the bright-bright, dark-bright combinations of a one-soliton solution (1SS) and two-soliton solutions (2SS) for an n-coupled NLSE with variable coefficients and gain. Crucial properties of two-soliton (dark-bright pair) interactions, such as elastic and inelastic interactions and the dynamics of soliton bound states, are studied using asymptotic analysis and graphical analysis. We show that a bright 2-soliton, in addition to elastic interactions, also exhibits multiple inelastic interactions. A dark 2-soliton, on the other hand, exhibits only elastic interactions. We also observe a breatherlike structure of a bright 2-soliton, a feature that become prominent with gain and disappears as the amplitude acquires a minimum value, and after that the solitons remain parallel. The dark 2-soliton, however, remains parallel irrespective of the gain. The results found by us might be useful for applications in soliton control, a fiber amplifier, all optical switching, and optical computing.
我们研究具有可变系数和增益的耦合非线性薛定谔方程（NLSEs）。耦合NLSE是光孤子在多模光纤介质或光纤阵列中传播及其相互作用的模型方程。通过使用广田双线性方法，我们得到了具有可变系数和增益的n耦合NLSE的单孤子解（1SS）和双孤子解（2SS）的亮-亮、暗-亮组合。利用渐近分析和图形分析研究了双孤子（暗-亮对）相互作用的关键特性，如弹性和非弹性相互作用以及孤子束缚态的动力学。我们表明，亮双孤子除了弹性相互作用外，还表现出多种非弹性相互作用。另一方面，暗双孤子仅表现出弹性相互作用。我们还观察到亮双孤子的类呼吸结构，该特征随着增益而变得突出，并在振幅达到最小值时消失，此后孤子保持平行。然而，暗双孤子无论增益如何都保持平行。我们发现的结果可能对孤子控制、光纤放大器、全光开关和光计算中的应用有用。
