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Title: When linear stability does not exclude nonlinear instability

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:
 [1] ;  [2] ;  [3]
  1. Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. McMaster Univ., Hamilton, ON (Canada)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
OSTI Identifier:
1233191
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
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)
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING