When linear stability does not exclude nonlinear instability

Kevrekidis, P. G.; Pelinovsky, D. E.; Saxena, A.

doi:10.1103/PhysRevLett.114.214101

Title: When linear stability does not exclude nonlinear instability

Journal Article · Fri May 29 00:00:00 EDT 2015 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.114.214101· OSTI ID:1233191

Kevrekidis, P. G. ^[1]; Pelinovsky, D. E. ^[2]; Saxena, A. ^[3]

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)

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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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: 2014/133; 2839; FA9550-12-1-0332; AC52-06NA25396

OSTI ID:: 1233191

Alternate ID(s):: OSTI ID: 1193887

Report Number(s):: LA-UR-14-29116; PRLTAO; TRN: US1600428

Journal Information:: Physical Review Letters, Vol. 114, Issue 21; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 17 works

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