When linear stability does not exclude nonlinear instability
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.
- Authors:
-
- Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- McMaster Univ., Hamilton, ON (Canada)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1233191
- Alternate Identifier(s):
- OSTI ID: 1193887
- Report Number(s):
- LA-UR-14-29116
Journal ID: ISSN 0031-9007; PRLTAO; TRN: US1600428
- Grant/Contract Number:
- 2014/133; 2839; FA9550-12-1-0332; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 114; Journal Issue: 21; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING
Citation Formats
Kevrekidis, P. G., Pelinovsky, D. E., and Saxena, A. When linear stability does not exclude nonlinear instability. United States: N. p., 2015.
Web. doi:10.1103/PhysRevLett.114.214101.
Kevrekidis, P. G., Pelinovsky, D. E., & Saxena, A. When linear stability does not exclude nonlinear instability. United States. https://doi.org/10.1103/PhysRevLett.114.214101
Kevrekidis, P. G., Pelinovsky, D. E., and Saxena, A. Fri .
"When linear stability does not exclude nonlinear instability". United States. https://doi.org/10.1103/PhysRevLett.114.214101. https://www.osti.gov/servlets/purl/1233191.
@article{osti_1233191,
title = {When linear stability does not exclude nonlinear instability},
author = {Kevrekidis, P. G. and Pelinovsky, D. E. and Saxena, A.},
abstractNote = {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.},
doi = {10.1103/PhysRevLett.114.214101},
journal = {Physical Review Letters},
number = 21,
volume = 114,
place = {United States},
year = {Fri May 29 00:00:00 EDT 2015},
month = {Fri May 29 00:00:00 EDT 2015}
}
Web of Science
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