We investigate wave collapse ruled by the generalized nonlinear Schro¨dinger (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.

Wave instabilities in the presence of non vanishing background in nonlinear Schrodinger systems

TRILLO, Stefano
Primo
;
2014

Abstract

We investigate wave collapse ruled by the generalized nonlinear Schro¨dinger (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.
2014
Trillo, Stefano; Totero, J. S.; Fratalocchi, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2334552
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