标题： 连续波、暗孤子和涡旋中的自发对称性破缺在线性耦合的双模系统中 显示英文标题

标题： Spontaneous symmetry breaking in continuous waves, dark solitons, and vortices in linearly coupled bimodal systems

摘要： 我们引入了一个模型，该模型描述了两个组分的共传播，这两个组分代表光纤中光的圆偏振态，它们之间的非线性排斥相对强度为g = 2，并且存在线性耦合。 也考虑了一个更一般的耦合Gross-Pitaevskii（GP）方程系统，其中g ≠ 2且组分之间存在线性混合。 后者以一维和二维（1D和2D）形式引入。 一个新发现是在g > 1的情况下，双模连续波（CW）状态的自发对称性破缺（SSB）（在没有线性耦合的情况下，这对应于非线性相互作用组分的不相容性）。 SSB由一个精确的不对称CW解表示。 在g = 3的情况下，还找到了支持不对称CW背景的稳定暗孤子（DSs）的精确解。 对于g ≠ 3的情况，产生了支持相同背景的稳定DSs的数值解。 此外，我们确定了一个参数区域，在该区域内，完全相容（对称）的CW背景在核心中保持稳定的DSs并具有内部SSB（组分之间的分离）。 在二维情况下，GP系统会产生具有组分间偏移和各向同性破坏的稳定涡旋态。 这些涡旋包括由不对称CW背景施加的组分间偏移的涡旋，以及由对称背景支持的状态，在这些状态中，两个组分的涡旋核心表现出内在的偏移（分裂）。 显示英文摘要

摘要： We introduce a model governing the copropagation of two components which represent circular polarizations of light in the optical fiber with relative strength g = 2 of the nonlinear repulsion between the components, and linear coupling between them. A more general system of coupled Gross-Pitaevskii (GP) equations, with g =/= 2 and the linear mixing between the components, is considered too. The latter system is introduced in its one- and two-dimensional (1D and 2D) forms. A new finding is the spontaneous symmetry breaking (SSB) of bimodal CW (continuous-wave) states in the case of g > 1 (in the absence of the linear coupling, it corresponds to the immiscibility of the nonlinearly interacting components). The SSB is represented by an exact asymmetric CW solution. An exact solution is also found, in the case of g = 3, for stable dark solitons (DSs) supported by the asymmetric CW background. For g =/= 3, numerical solutions are produced for stable DSs supported by the same background. Moreover, we identify a parameter domain where the fully miscible (symmetric) CW background maintains stable DSs with the inner SSB (separation between the components) in its core. In 2D, the GP system produces stable vortex states with a shift between the components and broken isotropy. The vortices include ones with the inter-component shift imposed by the asymmetric CW background, and states supported by the symmetric background, in which the intrinsic shift (splitting) is exhibited by vortical cores of the two components.