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DOE OSTI · 1233191

When linear stability does not exclude nonlinear instability

Kevrekidis, P. G.·Pelinovsky, D. E.·Saxena, A.
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Abstract

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. In this study, this instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensional lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.

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74 ATOMIC AND MOLECULAR PHYSICS97 MATHEMATICS AND COMPUTING

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BibTeXRIS

Kevrekidis, P. G., Pelinovsky, D. E., Saxena, A.. 2015-05-29. When linear stability does not exclude nonlinear instability. https://doi.org/10.1103/physrevlett.114.214101

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