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Article: Multistable dissipative structures pinned to dual hot spots

TitleMultistable dissipative structures pinned to dual hot spots
Authors
Issue Date2011
PublisherAmerican Physical Society. The Journal's web site is located at http://pre.aps.org
Citation
Physical Review E - Statistical, Nonlinear, And Soft Matter Physics, 2011, v. 84 n. 6, article no. 066609 How to Cite?
AbstractWe analyze the formation of one-dimensional localized patterns in a nonlinear dissipative medium including a set of two narrow "hot spots" (HSs), which carry the linear gain, local potential, cubic self-interaction, and cubic loss, while the linear loss acts in the host medium. This system can be realized as a spatial-domain one in optics and also in Bose-Einstein condensates of quasiparticles in solid-state settings. Recently, exact solutions were found for localized modes pinned to the single HS represented by the δ function. The present paper reports analytical and numerical solutions for coexisting two- and multipeak modes, which may be symmetric or antisymmetric with respect to the underlying HS pair. Stability of the modes is explored through simulations of their perturbed evolution. The sign of the cubic nonlinearity plays a crucial role: in the case of the self-focusing, only the fundamental symmetric and antisymmetric modes, with two local peaks tacked to the HSs, and no additional peaks between them, may be stable. In this case, all the higher-order multipeak modes, being unstable, evolve into the fundamental ones. Stability regions for the fundamental modes are reported. A more interesting situation is found in the case of the self-defocusing cubic nonlinearity, with the HS pair giving rise to a multistability, with up to eight coexisting stable multipeak patterns, symmetric and antisymmetric ones. The system without the self-interaction, the nonlinearity being represented only by the local cubic loss, is investigated too. This case is similar to those with the self-focusing or defocusing nonlinearity, if the linear potential of the HS is, respectively, attractive or repulsive. An additional feature of the former setting is the coexistence of the stable fundamental modes with robust breathers. © 2011 American Physical Society.
Persistent Identifierhttp://hdl.handle.net/10722/149109
ISSN
2014 Impact Factor: 2.288
2015 SCImago Journal Rankings: 0.999
ISI Accession Number ID
Funding AgencyGrant Number
Council of Hong KongHKU7120/08E
Funding Information:

Partial financial support of this work has been provided by Contract HKU7120/08E from the Research Grants Council of Hong Kong.

References

 

DC FieldValueLanguage
dc.contributor.authorTsang, CHen_HK
dc.contributor.authorMalomed, BAen_HK
dc.contributor.authorChow, KWen_HK
dc.date.accessioned2012-06-22T06:23:46Z-
dc.date.available2012-06-22T06:23:46Z-
dc.date.issued2011en_HK
dc.identifier.citationPhysical Review E - Statistical, Nonlinear, And Soft Matter Physics, 2011, v. 84 n. 6, article no. 066609en_HK
dc.identifier.issn1539-3755en_HK
dc.identifier.urihttp://hdl.handle.net/10722/149109-
dc.description.abstractWe analyze the formation of one-dimensional localized patterns in a nonlinear dissipative medium including a set of two narrow "hot spots" (HSs), which carry the linear gain, local potential, cubic self-interaction, and cubic loss, while the linear loss acts in the host medium. This system can be realized as a spatial-domain one in optics and also in Bose-Einstein condensates of quasiparticles in solid-state settings. Recently, exact solutions were found for localized modes pinned to the single HS represented by the δ function. The present paper reports analytical and numerical solutions for coexisting two- and multipeak modes, which may be symmetric or antisymmetric with respect to the underlying HS pair. Stability of the modes is explored through simulations of their perturbed evolution. The sign of the cubic nonlinearity plays a crucial role: in the case of the self-focusing, only the fundamental symmetric and antisymmetric modes, with two local peaks tacked to the HSs, and no additional peaks between them, may be stable. In this case, all the higher-order multipeak modes, being unstable, evolve into the fundamental ones. Stability regions for the fundamental modes are reported. A more interesting situation is found in the case of the self-defocusing cubic nonlinearity, with the HS pair giving rise to a multistability, with up to eight coexisting stable multipeak patterns, symmetric and antisymmetric ones. The system without the self-interaction, the nonlinearity being represented only by the local cubic loss, is investigated too. This case is similar to those with the self-focusing or defocusing nonlinearity, if the linear potential of the HS is, respectively, attractive or repulsive. An additional feature of the former setting is the coexistence of the stable fundamental modes with robust breathers. © 2011 American Physical Society.en_HK
dc.languageengen_US
dc.publisherAmerican Physical Society. The Journal's web site is located at http://pre.aps.orgen_HK
dc.relation.ispartofPhysical Review E - Statistical, Nonlinear, and Soft Matter Physicsen_HK
dc.rightsPhysical Review E. Copyright © American Physical Society.en_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleMultistable dissipative structures pinned to dual hot spotsen_HK
dc.typeArticleen_HK
dc.identifier.emailChow, KW:kwchow@hku.hken_HK
dc.identifier.authorityChow, KW=rp00112en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1103/PhysRevE.84.066609en_HK
dc.identifier.pmid22304213-
dc.identifier.scopuseid_2-s2.0-84855297333en_HK
dc.identifier.hkuros200238en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84855297333&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume84en_HK
dc.identifier.issue6en_HK
dc.identifier.spage066609-1en_US
dc.identifier.epage066609-11en_US
dc.identifier.eissn1550-2376-
dc.identifier.isiWOS:000298679300011-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridTsang, CH=36187480500en_HK
dc.identifier.scopusauthoridMalomed, BA=35555126200en_HK
dc.identifier.scopusauthoridChow, KW=13605209900en_HK
dc.customcontrol.immutablejt 1301314-

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