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• W2012184471 endingPage "140" @default.
• W2012184471 startingPage "103" @default.
• W2012184471 abstract "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 Schrödinger equation, 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." @default.
• W2012184471 created "2016-06-24" @default.
• W2012184471 creator A5026725553 @default.
• W2012184471 creator A5035172429 @default.
• W2012184471 creator A5069676216 @default.
• W2012184471 date "1999-01-01" @default.
• W2012184471 modified "2023-09-26" @default.
• W2012184471 title "Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability" @default.
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• W2012184471 doi "https://doi.org/10.1088/0951-7715/12/1/007" @default.
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