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Unpublished Paper
When Does Linear Stability Not Exclude Nonlinear Instability?
Physical Review Letters (2015)
  • Panos Kevrekidis
  • D. E. Pelinovsky
  • A. Saxena
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. 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.
Disciplines
Publication Date
May, 2015
Comments
Prepublished version downloaded from ArXiv. Published version is located at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.214101
Citation Information
Panos Kevrekidis, D. E. Pelinovsky and A. Saxena. "When Does Linear Stability Not Exclude Nonlinear Instability?" Physical Review Letters (2015)
Available at: http://works.bepress.com/panos_kevrekidis/275/