Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
PRIMALIGHT Research Group
KAUST Grant NumberCRG-1-2012-FRA-005)
Online Publication Date2014-12-03
Print Publication Date2015-05
Permanent link to this recordhttp://hdl.handle.net/10754/344394
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AbstractWe investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.
CitationWave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems 2014, 4:7285 Scientific Reports
SponsorsWe acknowledge funding from Italian Ministry of University and Research (MIUR, grant PRIN 2012BFNWZ2) and KAUST (Award No. CRG-1-2012-FRA-005).
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