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Matter-wave solitons for a periodic piecewise-constant nonlinearity | | A. S. Rodrigues
; P. G. Kevrekidis
; Mason A. Porter
; D. J. Frantzeskakis
; P. Schmelcher
; A. R. Bishop
; | | Rating: | Visitors: 5/5 (1 visitor) | | Date: |
6 Dec 2007 | | Abstract: | Motivated by recent proposals of ’’collisionally inhomogeneous’’
Bose-Einstein condensates (BECs), which have a spatially modulated scattering
length, we study the existence and stability properties of bright and dark
matter-wave solitons of a BEC characterized by a piecewise constant scattering
length. We use a ’’stitching’’ approach to analytically approximate the
pertinent solutions of the underlying nonlinear Schr"odinger equation, by
matching the wavefunction and its derivatives at the interfaces of the
nonlinearity coefficient. General tools from the theory of perturbed
Hamiltonian systems are adapted to accurately quantify the stability of bright
and dark solitons. It is shown that solitons can only exist at the center of
the regions of the piecewise constant nonlinearity. In the case of bright
solitons stable and unstable configurations are possible whereas for dark
solitons all solitons are unstable, although through different mechanisms
depending on the soliton location. The analytical results are corroborated by
the findings of numerical computations. | | Source: | arXiv, 0712.0986 | | Services: | Forum | Review | PDF | Favorites | |
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