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Titlebook: Emergent Nonlinear Phenomena in Bose-Einstein Condensates; Theory and Experimen Panayotis G. Kevrekidis,Dimitri J. Frantzeskakis,R Book 200

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https://doi.org/10.1007/978-3-663-10841-2, the experiments have inspired theoretical work in many directions. A particular example is the work on solitary waves in dimensional crossovers induced by trapping potentials that restrict the geometry, as discussed in Chap. 7.
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https://doi.org/10.1007/978-3-319-75981-4ues. When the external potential is decaying at infinity, finite-dimensional reductions of the GP equation can be derived for modeling of dynamics of localized modes. When the external potential is confining, the GP equation can be recovered from the multi-particle linear Schrödinger equation.
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https://doi.org/10.1007/978-3-531-90720-8stal lattices, polarons and photons in optical fibers. Moreover, the BEC experimentalists have reached such a high level of accuracy to create in the lab, so to speak, paradigmatic Hamiltonians, which were first introduced as idealized theoretical models to study, among others, dynamical instabilities or quantum phase transitions.
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