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• W2074928055 abstract "We investigate the dynamics of traveling oscillating solitons of the cubic nonlinear Schrodinger (NLS) equation under an external spatiotemporal forcing of the form $f(x,t)=amathrm{exp}[iK(t)x]$. For the case of time-independent forcing, a stability criterion for these solitons, which is based on a collective coordinate theory, was recently conjectured. We show that the proposed criterion has a limited applicability and present a refined criterion which is generally applicable, as confirmed by direct simulations. This includes more general situations where $K(t)$ is harmonic or biharmonic, with or without a damping term in the NLS equation. The refined criterion states that the soliton will be unstable if the ``stability curve'' $p(v)$, where $p(t)$ and $v(t)$ are the normalized momentum and the velocity of the soliton, has a section with a negative slope. In the case of a constant $K$ and zero damping, we use the collective coordinate solutions to compute a ``phase portrait'' of the soliton where its dynamics is represented by two-dimensional projections of its trajectories in the four-dimensional space of collective coordinates. We conjecture, and confirm by simulations, that the soliton is unstable if a section of the resulting closed curve on the portrait has a negative sense of rotation." @default.
• W2074928055 created "2016-06-24" @default.
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• W2074928055 date "2011-08-25" @default.
• W2074928055 modified "2023-10-03" @default.
• W2074928055 title "Refined empirical stability criterion for nonlinear Schrödinger solitons under spatiotemporal forcing" @default.
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• W2074928055 doi "https://doi.org/10.1103/physreve.84.026614" @default.
• W2074928055 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/21929135" @default.
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