一个允许平顶孤子的纯Kerr非线性模型
A purely Kerr nonlinear model admitting flat-top solitons
摘要：
我们阐述了一个和两个维（1D和2D）的自排斥立方非线性介质模型，其局部强度受到空间调制，承认存在各种类型的平顶孤子，包括基本的，1D多极，和2D涡旋。以前，这种类型的孤子只产生的模型与竞争的非线性。本设置可以在光学和玻色-爱因斯坦凝聚体中实现。一维的版本产生了一个精确的解析解稳定的平顶孤子，和一般的家庭可以预测的手段，通过的Fermas-Fermi近似。通过线性稳定性分析和直接模拟分析了平顶孤子的稳定性。具有$k=1$和$2$节点的基本孤子和一维多极子以及具有缠绕数$m=1$的涡旋是完全稳定的。对于具有$k\geq 3$的多极子和具有$m\geq 2$的涡，在它们的参数空间中确定了稳定性和不稳定性的交替条纹。
英文摘要：
We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including fundamental ones, 1D multipoles, and 2D vortices. Previously, solitons of this type were only produced by models with competing nonlinearities. The present setting may be implemented in optics and Bose-Einstein condensates. The 1D version gives rise to an exact analytical solution for stable flat-top solitons, and generic families may be predicted by means of the Thomas-Fermi approximation. Stability of the obtained flat-top solitons is analyzed by means of linear-stability analysis and direct simulations. Fundamental solitons and 1D multipoles with $k=1$ and $2$ nodes, as well as vortices with winding number $m=1$, are completely stable. For multipoles with $k\geq 3$ and vortices with $m\geq 2$, alternating stripes of stability and instability are identified in their parameter spaces.
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