标题： 二维和三维非线性法拉第共振中的振子 显示英文标题

标题： Two and three-dimensional oscillons in nonlinear Faraday resonance

摘要： 我们研究了一个简单模型系统中表现出非线性法拉第共振的二维和三维局部振荡模式。相应的振幅方程被证明具有精确的孤子解，这些解在三维情况下被发现总是不稳定的。相反，二维孤子在一定的参数范围内被证明是稳定的；因此，阻尼和参数驱动能够抑制二维空间中孤子的非线性爆裂和色散衰减。负反馈回路通过将孤子的相位（与驱动器耦合）从属于其振幅和宽度来实现。 显示英文摘要

摘要： We study 2D and 3D localised oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.