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.
Highlights
We investigate wave collapse ruled by the generalized nonlinear Schrodinger (NLS) equation in 111 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up
Many physical classical and quantum systems need to be described in terms of generalized NLS equation which accounts for higher-order nonlinearities
Such higher-order terms arise from different physical mechanisms in nonlinear optics, dynamics of superuids[26], or quantum condensed systems where they are related to higher-order atom-atom interactions[27,28,29]
Summary
Wave instabilities in the presence of non vanishing background in nonlinear Schrodinger systems. We investigate wave collapse ruled by the generalized nonlinear Schrodinger (NLS) equation in 111 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. 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. Our aim in this paper is to establish a novel criterion for collapse valid for solutions of this type, and study the dynamics across the threshold for blow-up This allows us to reveal a new instability scenario where opposite behaviors, such as blowup or decay into a dispersive shock wave, can be controlled by means of an arbitrarily weak perturbation which controls the variation of the power (or mass) integral of a launched perturbed solitary wavepacket. We start from the following gNLS equation in dimensionless units i
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