标题： 孤子管理用于超短脉冲：具有阻尼类似扰动的Fokas-Lenells方程的暗孤子和反暗孤子以及等价于自旋系统的规范等价系统 显示英文标题

标题： Soliton Management for ultrashort pulse: dark and anti-dark solitons of Fokas-Lenells equation with a damping like perturbation and a gauge equivalent spin system

摘要： 我们使用Fokas-Lenells方程（FLE）在不同色散、非线性效应和扰动下研究超短光脉冲的传播。这种系统可以称为孤子管理（SM）方案。首先，在一个规范变换后，通过变量的平移，我们将SM下的FLE转换为一种简化形式，该形式类似于Davydova和Lashkin为等离子体波给出的方程，我们将这种形式称为DLFLE。然后，我们通过引入一个辅助函数，在非消失背景中为DLFLE提出双线性化，这将DLFLE转化为三个双线性方程。我们求解这些方程，得到DLFLE的暗孤子和反暗孤子一孤子解（1SS）。从这里，通过解的逆变换，我们得到FLE的1SS，并探讨在不同SM方案下的孤子行为。之后，我们得到DLFLE的暗孤子和反暗孤子二孤子解（2SS），并通过渐近分析确定个体孤子相互作用时的相位偏移。然后，我们得到FLE的2SS，并表示不同SM方案下的孤子图。之后，我们介绍了确定DLFLE和FLE的N孤子解（NSS）的过程。后来，我们为DLFLE引入了一个Lax对，并通过规范变换将系统的谱问题转换为等效自旋系统的谱问题，该系统称为Landau-Lifshitz（LL）系统。LL方程（LLE）有潜力提供关于系统各种非线性结构和特性的信息。 显示英文摘要

摘要： We investigate the propagation of an ultrashort optical pulse using Fokas-Lenells equation (FLE) under varying dispersion, nonlinear effects and perturbation. Such a system can be said to be under soliton management (SM) scheme. At first, under a gauge transformation, followed by shifting of variables, we transform FLE under SM into a simplified form, which is similar to an equation given by Davydova and Lashkin for plasma waves, we refer to this form as DLFLE. Then, we propose a bilinearization for DLFLE in a non-vanishing background by introducing an auxiliary function which transforms DLFLE into three bilinear equations. We solve these equations and obtain dark and anti-dark one-soliton solution (1SS) of DLFLE. From here, by reverse transformation of the solution, we obtain the 1SS of FLE and explore the soliton behavior under different SM schemes. Thereafter, we obtain dark and anti-dark two-soliton solution (2SS) of DLFLE and determine the shift in phase of the individual solitons on interaction through asymptotic analysis. We then, obtain the 2SS of FLE and represent the soliton graph for different SM scheme. Thereafter, we present the procedure to determine N-soliton solution (NSS) of DLFLE and FLE. Later, we introduce a Lax pair for DLFLE and through a gauge transformation we convert the spectral problem of our system into that of an equivalent spin system which is termed as Landau-Lifshitz (LL) system. LL equation (LLE) holds the potential to provide information about various nonlinear structures and properties of the system.