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

S. Trillo; J. S. Totero Gongora; Andrea Fratalocchi

doi:10.1038/srep07285

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

S. Trillo, J. S. Totero Gongora, Andrea Fratalocchi

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We 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.

Original language	English (US)
Journal	Scientific Reports
Volume	4
Issue number	1
DOIs	https://doi.org/10.1038/srep07285
State	Published - Dec 3 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): CRG-1-2012-FRA-005)
Acknowledgements: We 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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10.1038/srep07285

https://repository.kaust.edu.sa/bitstream/10754/344394/1/srep07285.pdf

Cite this

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title = "Wave instabilities in the presence of non vanishing background in nonlinear Schr{\"o}dinger systems",

abstract = "We investigate wave collapse ruled by the generalized nonlinear Schr{\"o}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.",

author = "S. Trillo and Gongora, {J. S. Totero} and Andrea Fratalocchi",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): CRG-1-2012-FRA-005) Acknowledgements: We 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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AU - Trillo, S.

AU - Gongora, J. S. Totero

AU - Fratalocchi, Andrea

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): CRG-1-2012-FRA-005) Acknowledgements: We acknowledge funding from Italian Ministry of University and Research (MIUR, grant PRIN 2012BFNWZ2) and KAUST (Award No. CRG-1-2012-FRA-005).

PY - 2014/12/3

Y1 - 2014/12/3

N2 - We 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.

AB - We 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.

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

Abstract

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