Matter-wave solitons with a periodic, piecewise-constant scattering length
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 periodic, piecewise-const...
| Main Authors: | , , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2008
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| _version_ | 1826289530247839744 |
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| author | Rodrigues, A Kevrekidis, P Porter, M Frantzeskakis, D Schmelcher, P Bishop, A |
| author_facet | Rodrigues, A Kevrekidis, P Porter, M Frantzeskakis, D Schmelcher, P Bishop, A |
| author_sort | Rodrigues, A |
| collection | OXFORD |
| description | 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 periodic, piecewise-constant scattering length. We use a "stitching" approach to analytically approximate the pertinent solutions of the underlying nonlinear Schrödinger equation by matching the wave function and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that stationary solitons must be centered in one of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations. © 2008 The American Physical Society. |
| first_indexed | 2024-03-07T02:30:16Z |
| format | Journal article |
| id | oxford-uuid:a6ff498a-6350-4ae0-87d5-8f6fcdd976ff |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:30:16Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:a6ff498a-6350-4ae0-87d5-8f6fcdd976ff2022-03-27T02:51:26ZMatter-wave solitons with a periodic, piecewise-constant scattering lengthJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a6ff498a-6350-4ae0-87d5-8f6fcdd976ffEnglishSymplectic Elements at Oxford2008Rodrigues, AKevrekidis, PPorter, MFrantzeskakis, DSchmelcher, PBishop, AMotivated 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 periodic, piecewise-constant scattering length. We use a "stitching" approach to analytically approximate the pertinent solutions of the underlying nonlinear Schrödinger equation by matching the wave function and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that stationary solitons must be centered in one of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations. © 2008 The American Physical Society. |
| spellingShingle | Rodrigues, A Kevrekidis, P Porter, M Frantzeskakis, D Schmelcher, P Bishop, A Matter-wave solitons with a periodic, piecewise-constant scattering length |
| title | Matter-wave solitons with a periodic, piecewise-constant scattering length |
| title_full | Matter-wave solitons with a periodic, piecewise-constant scattering length |
| title_fullStr | Matter-wave solitons with a periodic, piecewise-constant scattering length |
| title_full_unstemmed | Matter-wave solitons with a periodic, piecewise-constant scattering length |
| title_short | Matter-wave solitons with a periodic, piecewise-constant scattering length |
| title_sort | matter wave solitons with a periodic piecewise constant scattering length |
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