Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons
Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons
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DOI：
10.1103/physreve.54.5707
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发表时间：
1996-11-01
影响因子：
2.4
通讯作者：
Smirnov, YS
中科院分区：
文献类型：
--
作者：
Barashenkov, IV;Smirnov, YS
研究了无限长直线上的外驱动阻尼非线性薛定谔方程。在强迫振幅h和耗散系数γ两个控制参数的平面上构造了孤子解的存在性和稳定性图。对于h和gamma的一般值，有两个共存的孤立子，其中一个（psi（+））总是不稳定的。第二个孤子（psi（-））的分叉图取决于耗散系数：如果gamma < gamma（cr），psi（-）对小的h是稳定的，随着h的增加，通过Hopf分叉失去稳定性;如果gamma > gamma（cr），psi（-）对所有的h都是稳定的。在不稳定区域没有“稳定窗口”。我们表明，以前报道的稳定窗口发生时，方程被认为是在一个有限的（和小）的空间间隔。
We study the externally driven damped nonlinear Schrodinger equation on an infinite line. The existence and stability chart for its soliton solution is constructed on the plane of two control parameters: the forcing amplitude h and the dissipation coefficient gamma. For generic values of h and gamma there are two coexisting solitons, one of which (psi(+)) is always unstable. The bifurcation diagram of the second soliton (psi(-)) depends on the dissipation coefficient: if gamma < gamma(cr), the psi(-) is stable for small h and loses its stability via a Hopf bifurcation as h is increased; if gamma > gamma(cr), the psi(-) is stable for all h. There are no ''stability windows'' in the unstable region. We show that the previously reported stability windows occur only when the equation is considered on a finite (and small) spatial interval.