标题： 节点二维孤子在非线性参量共振中 显示英文标题

标题： Nodal two-dimensional solitons in nonlinear parametric resonance

摘要： 参量驱动的阻尼非线性薛定谔方程作为平面上各种共振强迫振荡系统的振幅方程。 在本文中，我们考虑其节点孤子解。 我们表明，尽管对于足够大的阻尼系数，节点孤子对径向对称扰动是稳定的，但它们总是对方位扰动不稳定。 通过直接数值模拟研究了相应的破裂情景。 通常，节点解会分裂成对称的“项链”状的无节点孤子。 显示英文摘要

摘要： The parametrically driven damped nonlinear Schr\"odinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that although the nodal solitons are stable against radially-symmetric perturbations for sufficiently large damping coefficients, they are always unstable to azimuthal perturbations. The corresponding break-up scenarios are studied using direct numerical simulations. Typically, the nodal solutions break into symmetric "necklaces" of stable nodeless solitons.