The dynamics of a pair of three-dimensional matter-wave harmonic oscillators (HOs) coupled by a repulsive cubic nonlinearity is investigated through direct simulations of the respective GrossPitaevskii equations (GPEs) and with the help of the finite-mode Galerkin approximation (GA),which represents the two interacting wave functions by a superposition of 3 + 3 HO p -wave eigenfunctions with orbital and magnetic quantum numbers l = 1 and m = 1; 0; 1. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p -wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of non-coaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled GPEs agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l = 1.
Optical vortex trapping and annihilation by means of nonlinear Bessel beams in nonlinearly absorbing media
在非线性克尔介质中，当多光子吸收显著时，高阶非线性贝塞尔光束（NBB）中心的拓扑电荷m的涡旋可以稳定存在，并且无休止地存在。我们表明，m-充电NBB不仅是稳定的，但自发地形成从任何其他n-充电NBB和N“外国”旋涡的总电荷s随机嵌套在束截面，如果n + s = m。所有嵌套的旋涡合并在中心的原始NBB，这经历了模式转换的NBB，保持拓扑电荷和向内指向的功率电流，维持无衍射和无衰减的传播介质中的非线性吸收。我们预见到不同的应用，如创建稳定的，多电荷的旋涡没有严格的对齐要求，但通过自发的旋涡组合，混合波或粒子的旋涡可以引导，快速湮灭的旋涡偶极子，和清洁斑点光束的大量湮灭的旋涡。
Spontaneous symmetry breaking of fundamental states, vortices, and dipoles in two- and one-dimensional linearly coupled traps with cubic self-attraction
New exact spatially localized solutions of the (3 + 1) -dimensional nonlinear non-dissipative quasi-geostrophic potential vorticity equation for an exponential atmosphere
Solitons and Vortices in Two-dimensional Discrete Nonlinear Schrodinger Systems with Spatially Modulated Nonlinearity
我们考虑最近提出的模型[Phys. Rev. E 88，032905（2013）]的二维（2D）推广，其产生由散焦非线性支持的明亮离散孤子，散焦非线性的局部强度从中心到外围增长。我们从耦合消失的反连续（AC）极限出发，探索二维模型。在这个极限下，我们可以构造出各种各样的解，不仅包括单点激发，而且包括偶极和四极激发。此外，两个独立的家庭的解决方案进行了探讨：通常的“扩展”unstaggered亮孤子，其中所有的网站都在AC限制激发，具有相同的符号在整个晶格（他们代表最强大的状态支持的晶格，他们的1D对应物被认为是在上述工作中的1D亮孤子），和涡交叉，这是特定于2D设置。对于所有存在的状态，我们探索它们的稳定性（尽可能地分析）。通过直接模拟，展示了典型的不稳定性发展的情况。
