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Physical Sciences and Mathematics Commons™
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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
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Full-Text Articles in Physical Sciences and Mathematics
Vortex Nucleation In A Dissipative Variant Of The Nonlinear Schrödinger Equation Under Rotation, R. Carretero-González, Panayotis G. Kevrekidis, T. Kolokolnikov
Vortex Nucleation In A Dissipative Variant Of The Nonlinear Schrödinger Equation Under Rotation, R. Carretero-González, Panayotis G. Kevrekidis, T. Kolokolnikov
Mathematics and Statistics Department Faculty Publication Series
In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schrödinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential μ of the system, increasing proportionally toμ2/3. The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We …
Dark Solitons In External Potentials, De Pelinovsky, Pg Kevrekidis
Dark Solitons In External Potentials, De Pelinovsky, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We consider the persistence and stability of dark solitons in the Gross–Pitaevskii (GP) equation with a small decaying potential. We show that families of black solitons with zero speed originate from extremal points of an appropriately defined effective potential and persist for sufficiently small strength of the potential. We prove that families at the maximum points are generally unstable with exactly one real positive eigenvalue, while families at the minimum points are generally unstable with exactly two complex-conjugated eigenvalues with positive real part. This mechanism of destabilization of the black soliton is confirmed in numerical approximations of eigenvalues of the …