Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability
Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability
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参数驱动的 NLS 孤子在振荡不稳定发生后的动力学
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
D. Pelinovsky
中科院分区：
文献类型：
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作者：
N. Alexeeva;I. V. Barashenkov;D. Pelinovsky
保守和近保守系统中的孤立波可能由于两个内振动模的共振而变得不稳定。我们研究了参数驱动的、阻尼型的非线性Schreation，这是一个展示这种振荡不稳定性的原型系统。利用渐近多尺度展开，导出了描述弱耗散情况下孤子失稳和超临界动力学的非线性阶段的约化振幅方程。当分叉为Hopf型时，我们还推导出了强耗散情形下的振幅方程。对简化方程的分析表明，在无阻尼的情况下，时间周期的空间局部化结构受到非线性辐射的抑制。在这种情况下，不稳定的静止孤子要么演化成缓慢衰减的长寿命呼吸子，要么演化成幅度无限增长的辐射孤子。然而，增加一个小的阻尼值就足以产生一个稳定振荡的有限振幅孤子。PAC编号：0340K、0545、7530D
Solitary waves in conservative and near-conservative systems may become unstable due to a resonance of two internal oscillation modes. We study the parametrically driven, damped nonlinear Schrequation, a prototype system exhibiting this oscillatory instability. An asymptotic multi-scale expansion is used to derive a reduced amplitude equation describing the nonlinear stage of the instability and supercritical dynamics of the soliton in the weakly dissipative case. We also derive the amplitude equation in the strongly dissipative case, when the bifurcation is of the Hopf type. The analysis of the reduced equations shows that in the undamped case the temporally periodic spatially localized structures are suppressed by the nonlinearity-induced radiation. In this case the unstable stationary soliton evolves either into a slowly decaying long- lived breather, or into a radiating soliton whose amplitude grows without bound. However, adding a small damping is sufficient to bring about a stably oscillating soliton of finite amplitude. PACS numbers: 0340K, 0545, 7530D