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Emergence of unstable modes in an expanding domain for energy-conserving wave equations
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Law, K. J. H., Kevrekidis, P. G., Frantzeskakis, D. J. and Bishop, A. R. (2008) Emergence of unstable modes in an expanding domain for energy-conserving wave equations. Physics Letters A, Vol.372 (No.5). pp. 658-664. doi:10.1016/j.physleta.2007.07.082 ISSN 0375-9601.
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Official URL: http://dx.doi.org/10.1016/j.physleta.2007.07.082
Abstract
Motivated by recent work on instabilities in expanding domains in reaction–diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schrödinger equation in a finite domain and show how the expansion or contraction of the domain, under appropriate conditions, can destabilize its originally stable solutions through the modulational instability mechanism. Using both real and Fourier space diagnostics, we monitor and control the crossing of the instability threshold and, hence, the activation of the instability. We also consider how the manifestation of this mechanism is modified in a spatially inhomogeneous setting, namely in the presence of an external parabolic potential, which is relevant to trapped Bose–Einstein condensates.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Physics Letters A | ||||
Publisher: | Elsevier Science BV | ||||
ISSN: | 0375-9601 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.372 | ||||
Number: | No.5 | ||||
Page Range: | pp. 658-664 | ||||
DOI: | 10.1016/j.physleta.2007.07.082 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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